Exploring novel radiotherapy techniques with Monte Carlo simulation and measurement

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2 Exploring novel radiotherapy techniques with Monte Carlo simulation and measurement Heidi Nettelbeck A thesis submitted in fulfilment of the requirements for the award of the degree Doctor of Philosophy School of Engineering Physics University of Wollongong Australia 2009 Thesis supervisors: Doctor George J. Takacs and Professor Anatoly B. Rosenfeld

3 ABSTRACT This work is the first comprehensive investigation of potential changes in the radiobiological effectiveness of clinical photon beams caused by a redistribution of electrons in a magnetic field. It is also a fundamental study of both the influence of magnetic fields on the peak-to-valley dose ratio of microbeams and the accuracy of theoretical modelling for dose planning in Microbeam Radiation Therapy (MRT). The application of a strong transverse magnetic field to a volume undergoing irradiation by a photon beam can produce localised regions of dose enhancement and dose reduction. Results from Monte Carlo PENELOPE simulation show regions of enhancement and reduction of as much as % and 77% respectively for magnetic fields of to 00 T applied to Co 60, 6, 0, 5, and 24 MV photon beams. The dose redistribution is shown to occur predominantly through an alteration in the lower energy electron population, which may correspond to a change in the relative biological effectiveness. In MRT, an experimental and theoretical investigation of the influence of transverse and longitudinal magnetic fields on the lateral dose profile and peak-to-valley dose ratio (PVDR) of microbeams is presented. Results show that longitudinal magnetic fields greater than 0 T are needed to produce an effect. Strong transverse magnetic fields, on the other hand, have no influence on microbeam profiles. The radiation response of the edge-on MOSFET and its ability to measure dose profiles of monoenergetic and polyenergetic microbeams are also investigated. Simulations investigating the dependence of microbeam dose profiles on the accuracy of beamline modelling (i.e. synchrotron source, multislit collimator, and beam divergence) are also presented. Results show the asymmetric collimator construction is responsible for a 0% variation in the full-width at half-maximum of microbeams which affects the PVDR. Modelling the distributed source and beam divergence increases the penumbral dose by almost 30%. The influence of the collimator alignment, interaction medium, and the height of scoring regions on the PVDR are also investigated. i

4 CERTIFICATION I, Heidi Nettelbeck, declare that this thesis, submitted in fulfilment of the requirements for the award of Doctor of Philosophy, in School of Engineering Physics, University of Wollongong, is wholly my own work unless otherwise referenced or acknowledged. The document has not been submitted for qualifications at any other academic institution. Heidi Nettelbeck April 4, 2009 ii

5 ACKNOWLEDGEMENTS I would like to acknowledge my supervisors, Doctor George Takacs and Professor Anatoly Rosenfeld and thank them for their guidance throughout the course of this project. In particular, I thank George for his assistance with the Monte Carlo aspects of this work, and Anatoly for sharing his in-depth knowledge of radiation dosimetry. My appreciation also extends to Doctor Michael Lerch at the Centre for Medical Radiation Physics, University of Wollongong, and the scientists on the ID-7 biomedical beamline at the European Synchrotron Radiation Facility in Grenoble, France, for their assistance with the magneto-mrt experiments. I would also like to acknowledge Terry Braddock and Brad Oborn for constructing the magnet devices used in these experiments, and Doctor José Fernández-Varea for identifying the origin of a spurious peak in the simulated electron spectra. I also thank the postgraduate students and staff in the School of Physics for their lively discussions and friendship over the years. I have fond memories of mountain and beach runs with George and Neil, and music sessions in the lab. Finally, I thank my friends and family for their ongoing encouragement. A special thank you to Daniel for his unfailing patience and support, and God for carrying me to the end. iii

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7 TABLE OF CONTENTS Page LIST OF TABLES vii LIST OF FIGURES PUBLICATION LIST viii xix CHAPTER Introduction Background and motivation Objectives and scope of this research Thesis outline Radiation transport and the Monte Carlo PENELOPE code Interactions of radiation with matter Photon interactions Electron interactions Monte Carlo PENELOPE code Brief outline of code structure and operation Particle transport Electron transport in magnetic fields Influence of a transverse magnetic field on the dose distribution in photon beam radiotherapy Introduction Simulation methods Simulation results Effect of the magnetic field strength Effect of the photon beam energy Effect of the depth and thickness of magnetic field Discussion Conclusion Effect of a transverse magnetic field on the electron distribution of highenergy photon beams Introduction Simulation methods Simulation results and discussion Influence of a magnetic field on electron spectra below MeV Influence of a magnetic field on electron spectra below 0 kev Influence of a magnetic field on electron spectra below kev Effect of magnetic field on the w-values of electrons Effect of magnetic field on the spatial distribution of electrons 78 v

8 4.4 Conclusion MOSFET dosimetry in Microbeam Radiation Therapy (MRT) Introduction Microbeam Radiation Therapy (MRT) MOSFET dosimetry in MRT MRT at the ESRF ID-7 biomedical beamline Experimental and simulation methods Results and discussion Radiation response of MOSFET dosimeters Measured and simulated dose profiles of microbeams Measured and simulated peak-to-valley dose ratios (PVDRs) Conclusion Magneto-MRT: influence of a magnetic field on microbeam profiles Introduction Materials and methods Magneto-MRT with a transverse magnetic field Magneto-MRT with a longitudinal magnetic field Magneto-MRT Monte Carlo simulations Results and Discussion Effect of a transverse magnetic field on microbeam profiles Effect of a longitudinal magnetic field on microbeam profiles Conclusion A Monte Carlo study of the influence of MRT beamline components on microbeam profiles Introduction Materials and Methods Results and discussion Effect of the beam divergence Effect of the multislit collimator Effect of the source model Effect of the multislit collimator lateral offset Effect of the simulation model Effect of the multislit collimator alignment Effect of the collimator design Effect of the interaction medium Effect of the height of scoring regions Conclusion Conclusion APPENDICES A High current pulser for the magnet coil in magneto-mrt experiments REFERENCES vi

9 LIST OF TABLES Table Page 3. Range of electrons in water as a function of energy Comparison of the maximum DPF for a 5 MV beam with B = to 00 T Comparison of the minimum DPF for a 5 MV beam with B = to 00 T Comparison of the maximum DPF for a 5 MV beam with B = to 00 T using bin depths of 0. and 0.2 cm Comparison of the minimum DPF for a 5 MV beam with B = to 00 T, and bin depths of 0. and 0.2 cm Comparison of the maximum DPF for different photon beams with B = 5 T Comparison of the minimum DPF for different photon beams with B = 5 T Binding energies of hydrogen and oxygen Energies and probabilities of Auger electron production in water Peak and valley doses and PVDR of the central peak (peak 2) in an array of three microbeams. Peak and valley doses were measured with Gafchromic film at 0. and 0.2 cm depth (in perspex) in the presence and absence of a T longitudinal magnetic field, B vii

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11 LIST OF FIGURES Figure Page 2. Cross sections for photon interactions in water. Data extracted from the NIST XCOM Photon Cross Sections database Angular distribution of Compton scattered photons calculated from the Klein-Nishina cross section. A plot of the intensity of a scattered photon of 0., 0.5,, 5, 0, and 5 MeV interacting with a free electron at the centre of this graph Angular distribution of Compton scattered electrons calculated from the Klein-Nishina cross section. A plot of the intensity of the electrons produced from Compton scattered photons of 0., 0.5,, 5, 0, and 5 MeV. 3. Energy dependence of the range, mean free path, and radius of curvature of an electron moving in magnetic field. The range of an electron (in water) as a function of energy is based on the data in table Effect of a slice of 5 T transverse magnetic field (7 to 9 cm depth) on the: (a) depth-dose, and (b) dose perturbation factor (DPF) of a 0 MV beam (direction of magnetic field is out of the page) Figure (a) and (b) show the input photon beam spectrum used for simulations with 6 and 0 MV beams, respectively Figure (c) and (d) show the input photon beam spectrum used for simulations with 5 and 24 MV beams, respectively Dose distribution of a 5 MV beam (in water) subjected to a slice of, 2, 5, 0, 20 and 00 T transverse magnetic field (7 to 9 cm depth), using bin depths of: (a) 0.2 cm, and (b) 0. cm Effect of the elastic scattering parameters C and C 2 (C = C = C 2 ) on the dose deposition of a 5 MV beam (in water) subjected to a 2 T transverse magnetic field (7 to 9 cm depth) Dose distribution of Co 60, 6, 0, 5 and 24 MV photon beams (in water) subjected to a slice of 5 T transverse magnetic field (7 to 9 cm depth) Dose distribution of a 5 MV beam with a slice of 5 T transverse magnetic field (2 cm thick) applied at different depths in the water phantom Effect of the magnetic field thickness. Figures (a) and (b) show the effect on the depth-dose of a 5 MV beam when a 2, 5 and 0 T transverse magnetic field is applied at 7.5 to 8.5 cm and 7 to 9 cm depth (i.e. cm and 2 cm thick) in water, respectively Effect of the magnetic field thickness. Figures (c) and (d) show the effect on the depth-dose of a 5 MV beam when a 2, 5 and 0 T transverse magnetic field is applied at 6.5 to 9.5 cm and 6 to 0 cm depth (i.e. 3 cm and 4 cm thick) in water, respectively Effect of the magnetic field thickness. Figures (a) and (b) compare the effect of a 5 T transverse magnetic field of different thicknesses ( to 4 cm) on the depth-dose (in water) of a 6 and 0 MV beam respectively.. 38 ix

12 3.9 Effect of the magnetic field thickness. Figures (c) and (d) compare the effect of a 5 T transverse magnetic field of different thicknesses ( to 4 cm) on the depth-dose (in water) of a 5 and 24 MV beam respectively Influence of a magnetic field on the mean distance an electron travels along the beam direction from its origin at 6.9 cm depth Secondary electron spectrum of a 5 MV photon beam at different depths (5.5 to 0.5 cm) in water Relationship between relative biological effectiveness (RBE) and mean linear energy transfer (LET) for cell killing, where the three curves correspond to different levels of cell survival, or surviving fraction (SF) Figure (a) plots the absorption and scattering contributions towards the total attenuation of water. Figure (b) plots the PENELOPE atomic photoelectric cross sections of hydrogen (K shell) and oxygen (K, L, L 2, and L 3 shells) First generation electron spectra for polyenergetic and monoenergetic photon beams (in water). Figure (a) plots the first generation electron spectra for Co 60, 6, 0, and 5 MV beams. Corresponding electron spectra for, 5, 0, and 5 MeV monoenergetic photon beams are shown in figure (b) Secondary electron spectra (all generations) for a 5 MV beam with depth (in water). Figures (a) and (b) plot the electron spectra in the presence and absence of a slice of 5 T transverse magnetic field (7 to 9 cm depth), respectively Normalised electron spectra (below MeV) for a 5 MV beam. Figures (a) and (b) plot a ratio of the electron population in the presence and absence of a 2 and 5 T transverse magnetic field (7 to 9 cm depth), respectively Normalised electron spectra (below MeV) for a 5 MV beam. Figures (c) and (d) plot a ratio of the electron population in the presence and absence of a 0 and 20 T transverse magnetic field (7 to 9 cm depth), respectively Secondary electron spectra (below 0 kev) for a 5 MV beam. Figures (a) and (b) plot the electron spectra in five depth regions in the presence and absence of a 5 T transverse magnetic field (7 to 9 cm depth), respectively Normalised electron spectra (below 0 kev) for a 5 MV beam. A ratio of the electron population in five depth regions in the presence and absence of a 5 T transverse magnetic field (7 to 9 cm depth) Ratio of electron spectra (below 0 kev) for a 5 MV beam as a function of magnetic field. A ratio of the electron population in five depth regions in the presence and absence of a, 2, 3, 4, 5, 0, and 20 T transverse magnetic field (7 to 9 cm depth) Photon spectra (below 0 kev) for a 5 MV beam. Figures (a) and (b) plot the photon spectra with and without a 5 T transverse magnetic field (7 to 9 cm depth), respectively Electron spectra (below kev) for a 5 MV beam. Figures (a) and (b) plot the electron spectra with and without a 5 T transverse magnetic field (7 to 9 cm depth), respectively x

13 4. Normalised electron spectra (below kev) for a 5 MV beam. Figures (a) and (b) plot a ratio of the electron population in the presence and absence of a 2 and 5 T transverse magnetic field (7 to 9 cm depth), respectively Normalised electron spectra (below kev) for a 5 MV beam. Figures (c) and (d) plot a ratio of the electron population in the presence and absence of a 0 and 20 T transverse magnetic field (7 to 9 cm depth), respectively Spectra of atomic relaxation electrons and photons (in water) for a 5 MV beam. Figures (a) and (b) plot the spectra of atomic relaxation electrons with and without a 5 T transverse magnetic field (7 to 9 cm depth), respectively. Atomic relaxation photons are plotted in figure (c) Mean w-values of first generation electrons of the following photon beams: (a) Co 60, 6, 0, and 5 MV, and (b) 0., 0.5,, 5, 0, and 5 MeV Distance travelled by electrons before they are deviated from their initial trajectory by a given angle Distance electrons travel in water before the angle of deviation from their initial trajectory exceeds 25.8, 45.6, 60, and 90 degrees (i.e. w = 0.9, 0.7, 0.5, and zero). A plot of the accumulative electron population as a function of distance travelled from the origin is shown in figures (a), (b), and (c) for 0., 0.5, and MeV electrons, respectively Distance electrons travel in water before the angle of deviation from their initial trajectory exceeds 25.8, 45.6, 60, and 90 degrees (i.e. w = 0.9, 0.7, 0.5, and zero). A plot of the accumulative electron population as a function of distance travelled from the origin is shown in figures (d), (e), and (f) for 5, 0, and 5 MeV electrons, respectively Population and mean w-values of first generation electrons for 5 MV beam beyond 6.9 cm depth (in water) Magnetic field s influence on the interaction depths of electrons starting at 6.9 cm depth. Figure (a) plots the electrons mean z-ranges as a function of magnetic field. A ratio of the mean z-ranges with and without magnetic field is shown in figure (b), and a ratio of electrons with final positions downstream of their initial position (z > z start ) to those with final positions upstream (z < z start ) is plotted in figure (c) Magnetic field s influence on the lateral ranges of electrons starting at 6.9 cm depth. Figure (d) plots the mean y-ranges of electrons as a function of magnetic field. A ratio of the mean y-ranges with and without magnetic field is shown in figure (e), and a ratio of electrons with negative final y-positions (y < 0) to those with positive final y-positions (y > 0) is plotted in figure (f) Magnetic field s influence on the interaction depths of electrons starting at 7.5 cm depth. Figure (a) plots the electrons mean z-ranges as a function of magnetic field. A ratio of the mean z-ranges with and without magnetic field is shown in figure (b), and a ratio of electrons with final positions downstream of their initial position (z > z start ) to those with final positions upstream (z < z start ) is plotted in figure (c) xi

14 4.8 Magnetic field s influence on the lateral ranges of electrons starting at 7.5 cm depth. Figure (d) plots the mean y-ranges of electrons as a function of magnetic field. A ratio of the mean y-ranges with and without magnetic field is shown in figure (e), and a ratio of electrons with negative final y-positions (y < 0) to those with positive final y-positions (y > 0) is plotted in figure (f) Magnetic field s influence on the interaction depths of electrons starting at 8.5 cm depth. Figure (a) plots the electrons mean z-ranges as a function of magnetic field. A ratio of the mean z-ranges with and without magnetic field is shown in figure (b), and a ratio of electrons with final positions downstream of their initial position (z > z start ) to those with final positions upstream (z < z start ) is plotted in figure (c) Magnetic field s influence on the lateral ranges of electrons starting at 8.5 cm depth. Figure (d) plots the mean y-ranges of electrons as a function of magnetic field. A ratio of the mean y-ranges with and without magnetic field is shown in figure (e), and a ratio of electrons with negative final y-positions (y < 0) to those with positive final y-positions (y > 0) is plotted in figure (f) Magnetic field s influence on the interaction depths of electrons starting at 8.9 cm depth. Figure (a) plots the electrons mean z-ranges as a function of magnetic field. A ratio of the mean z-ranges with and without magnetic field is shown in figure (b), and a ratio of electrons with final positions downstream of their initial position (z > z start ) to those with final positions upstream (z < z start ) is plotted in figure (c) Magnetic field s influence on the lateral ranges of electrons starting at 8.9 cm depth. Figure (d) plots the mean y-ranges of electrons as a function of magnetic field. A ratio of the mean y-ranges with and without magnetic field is shown in figure (e), and a ratio of electrons with negative final y-positions (y < 0) to those with positive final y-positions (y > 0) is plotted in figure (f) Schematic diagram of a p-mosfet (Metal-Oxide-Semiconductor Field Effect Transistor) dosimeter Schematic diagram of the MOSFET reader. The MOSFET dosimeter is read out under a constant current I D with the gate and source grounded. The threshold voltage, V th, measured across the MOSFET is proportional to the dose deposited in the SiO 2 gate oxide The dose response of MOSFET dosimeters to effective radiation energy. The dose response (in free-air geometry) was normalised to that obtained with 6 MV X-rays from a medical linear accelerator X-ray energy spectrum for MRT measured at the ESRF ID-7 biomedical beamline Schematic diagram of the MRT setup at the ESRF ID-7 beamline Scanning electron microscope image of the REM TOT500 RADFET chip ( 0.5 mm 3 ), which shows the two low-sensitive MOSFETs, Q2 and Q3, and two high-sensitive MOSFETs, Q and Q4. The direction of the X-ray microbeam is indicated by the arrows Illustration of the MOSFET configuration used to scan the dose profiles of monoenergetic microbeams, where the beam direction is into the page. 2 xii

15 5.8 Radiation response of MOSFET dosimeters. Figure (a) plots the normalised response of a MOSFET(H) dosimeter subjected to s pulses of white beam radiation. The response of a MOSFET(L) dosimeter to s irradiations with a 50 kev beam is shown in figure (b) Radiation response of MOSFET dosimeters. Figure (c) plots the normalised response of a MOSFET(H) dosimeter subjected to s pulses of irradiation with a 50 kev beam. The response of a MOSFET(H) dosimeter to 25 0 s irradiations with a 00 kev beam is shown in figure (d) Dose profiles of monoenergetic microbeams measured at. cm depth (in perspex) with a MOSFET(L) dosimeter. Figures (a) and (b) show the dose profile of the central peak in an array of 24 microbeams (peak 2) for 30 and 50 kev beams, respectively Dose profiles of monoenergetic microbeams measured at. cm depth (in perspex) with a MOSFET(L) dosimeter. Figures (c) and (d) show the dose profile of the central peak in an array of 24 microbeams (peak 2) for 70 and 00 kev beams, respectively Dose profile of the central peak in an array of 24 microbeams (peak 2) obtained with the ESRF white beam and measured with a MOSFET(H) dosimeter at. cm depth (in perspex) Comparison of the dose profile of the central peak in an array of 24 microbeams (peak 2) measured with a MOSFET at. cm depth (in perspex) for the white beam and monoenergetic beams of 30, 50, 70, and 00 kev Simulated dose profile of the central microbeam in an array of 24 microbeams (peak 2) obtained at. cm depth (in perspex) for the white beam and monoenergetic beams of 30, 50, 70, and 00 kev Simulated penumbral and valley dose of a single microbeam, and the central microbeam (peak 2) in an array of 24 microbeams. Figures (a) and (b) plot the dose profile of a single microbeam and peak 2, respectively, at. cm depth (in perspex) for the white beam and monoenergetic beams of 30, 50, 70, and 00 kev Simulated microbeam profile showing the dose distribution according to the type of initial photon interaction. Figures (a) and (b) plot the dose contributions of a single microbeam at. cm depth (in perspex) for monoenergetic beams of 30 and 50 kev, respectively Simulated microbeam profile showing the dose distribution according to the type of initial photon interaction. Figures (c) and (d) plot the dose contributions of a single microbeam at. cm depth (in perspex) for monoenergetic beams of 70 and 00 kev, respectively Comparison of the Continuous Slowing Down Approximation (CSDA) range of electrons in silicon and perspex Photon interaction cross sections in silicon Measured PVDR of the central microbeam in an array of 24 (peak 2) calculated from peak and valley doses obtained at. cm depth (in perspex) for 30, 50, and 70 kev beams and the white beam (maximum intensity of 83 kev) xiii

16 5.8 Simulated PVDR of the central microbeam in an array of 24 (peak 2) calculated from the theoretical dose profiles at. cm depth (in perspex) for 30, 50, 70, and 00 kev beams and the white beam (maximum intensity of 83 kev) Measured PVDRs of microbeams 2, 7, and 22 (in an array of 24 microbeams) for the 50 kev and white beams, calculated from peak and valley dose measurements obtained with a MOSFET at. cm depth (in perspex) Simulated PVDRs of microbeams 2, 7, and 22 (in an array of 24 microbeams) for the 50 kev and white beams, calculated from the theoretical dose profiles obtained at. cm depth (in perspex). The 50 kev measured PVDRs (meas 50 kev) are also shown for comparison Simulated PVDRs for an array of 24 microbeams, calculated from the theoretical dose profiles obtained at. cm depth (in perspex) with the white beam and 30, 50, 70, and 00 kev monoenergetic beams Measured and simulated PVDRs with depth (in perspex) for the central peak in an array of three microbeams (peak 2) produced with a white beam. The measured PVDRs were obtained at 0.9,.9, and 2.8 cm depth, and the theoretical PVDRs at various depths up to.2 cm Simulated peak and valley doses for the central peak in an array of three microbeams (peak 2) up to 2.8 cm depth (in perspex). Peak and valley doses have been normalised to their maximum values Impact of different types of interaction on the lateral dose profile of a single microbeam (25 µm wide) obtained with the ESRF white beam. Curve plots the microbeam profile comprising all interaction contributions. Curves 2, 3, and 4 plot the profile with supression of the photoelectric effect, Compton scattering, and electron tracking, respectively Simulated first generation electron spectrum of the ESRF white beam (in perspex) Photos of the T transverse magnetic field device used for magneto-mrt experiments (direction of magnetic field is towards the handle). The magnet device (right) was mounted on the goniometer stage, where a perspex phantom containing a MOSFET was wedged between the magnet poles (left) Illustration of the T longitudinal magnetic field device used for magneto- MRT experiments. A 0.3 cm diameter hole was drilled through the centre of the permanent magnets to allow the passage of microbeams parallel to the direction of magnetic field Scatter contributions from different magnet materials. Figure (a) plots the depth-dose profile of a pencil beam simulated with different magnet materials (NdFeB, perspex, and air) in three regions along central axis: air cavity, perspex phantom, and air cavity 2. Figure (b) plots the depthdose profile with perspex replacing the air in cavity Effect of magnet scatter contributions on the radial dose. Figure (a) plots a ratio of the radial dose with and without NdFeB magnets, at the following depths: 2.48 cm (exit of air cavity ), 2.60 and 2.90 cm ( and 4 mm depth in perspex), and 3.02 cm (entrance to air cavity 2). Figures (b) and (c) plots the corresponding radial dose with perspex magnets instead of NdFeB, and perspex replacing the air in cavity xiv

17 6.7 Photo of the 2 T longitudinal magnetic field device used for magneto- MRT experiments. The device comprises a pair of cylindrical NdFeB permanent magnets with steel focus cones and a U-shaped iron circuit to maximise magnetic flux MATLAB simulation of the magnetic flux produced by the longitudinal magnetic field device. A maximum field of 2.2 T was calculated between the focus cones, which were separated by cm Photos of the magnet coil used for magneto-mrt experiments. The 828- turn copper coil was mounted on the goniometer (left), where the cylindrical perspex phantom (housing the MOSFET) was inserted into the air core and secured to a perspex block behind the coil (right) Oscilloscope output verifying the synchronisation of the current pulse (i.e. pulsed magnetic field) and the rectangular diode pulse (i.e. beam delivery) Oscilloscope output verifying the coincidence of the pulsed current (i.e. discharge of capacitors) and magnetic field. Delay between the current and diode pulses was adjusted to provide a maximum magnetic field during irradiation of the target Lateral dose profile of an array of three microbeams measured with a MOSFET at 0.9 cm depth (in perspex) in the presence of a T transverse magnetic field Effect of a T transverse magnetic field on the valley dose of an array of three microbeams. Figures (a) and (b) plot the dose profiles of valley regions V 2 and V 23 (i.e. left and right of the central microbeam, peak 2) respectively, measured with a MOSFET at 0.9 cm depth (in perspex) in the presence and absence of magnetic field Valley dose for an an array of three microbeams measured with a MOS- FET at 0.9,.9, and 2.8 cm depth (in perspex). Figures (a) and (b) plot the dose at the centre of valleys V 2 and V 23 (i.e. left and right of the central microbeam, peak 2) respectively, in the presence and absence of a T transverse magnetic field Peak dose and PVDR for the central microbeam in an array of three microbeams (peak 2) measured with a MOSFET at 0.9,.9, and 2.8 cm depth (in perspex), in the presence and absence of a T transverse magnetic field, is shown in figures (c) and (d) respectively. The PVDR was calculated using the dose at the centre of peak 2 and valleys V 2 and V 23 on either side Simulated effect of a transverse magnetic field on the dose profile of an array of three microbeams. A plot of the microbeam array scored between 0.8 and.0 cm depth (in perspex) in the presence and absence of a 2 and 00 T transverse magnetic field Dose profile of an array of three microbeams measured with Gafchromic film at 0., 0.2, 0.7,., and.2 cm depths (in perspex) in the absence of magnetic field Peak dose of the central microbeam in an array of three microbeams (peak 2) with depth. A plot of the peak dose measured with Gafchromic film at depths (in perspex) of 0., 0.2, 0.3, and 0.4 cm in the presence of a T longitudinal magnetic field, and 0., 0.2, 0.7,., and.2 cm in the absence of magnetic field xv

18 6.8 Effect of a T longitudinal magnetic field on the peak and valley doses of an array of three microbeams. Figures (a) and (b) show the peak and valley dose profiles, respectively, measured with Gafchromic film at 0.2 cm depth (in perspex) in the presence and absence of magnetic field Simulated effect of a longitudinal magnetic field on the dose profile of a single microbeam. A plot of the profile scored between.0 and.2 cm depth (in perspex) in the presence and absence of a 2, 0, 20, 50, and 00 T magnetic field Simulated effect of a longitudinal magnetic field on the dose profile of an array of three microbeams. Figure (a) shows the dose profile of the array scored between.0 and.2 cm depth (in perspex) in the presence and absence of a 2, 0, 20, 50, and 00 T magnetic field. A ratio of the dose profile with and without magnetic field is plotted in figure (b) Simulated effect of a longitudinal magnetic field on the PVDR of an array of three microbeams. A plot of the PVDR of the central microbeam against magnetic field strength, using the dose profiles scored between.0 and.2 cm depth (in perspex) Photo of the Tecomet R multislit collimator (left) which comprises two identical tungsten air stacks mounted in an aluminum frame. Each stack (right) contains 25 parallel, 00 µm wide, 8 mm deep apertures with 400 µm centre-to-centre spacing Illustration of the lateral offset of the multislit collimator stacks. Figure (a) illustrates the adjustment of microbeam width by laterally moving one stack relative to the other (as indicated by arrows). Figure (b) shows an enlargement of a single collimator element, comparing the photon transmission through the central collimator aperture (C) and the fifth apertures to the left and right of centre (L5 and R5 respectively) Illustration of the effect of multislit collimator alignment. Figure (a) shows the multislit collimator rotated through a small positive angle (with respect to the beam). Figure (b) shows an enlargement of a single collimator element, comparing the photon transmission through the central aperture (C) and the fifth apertures to the left and right of centre (L5 and R5 respectively) The influence of the beam divergence (i.e. source to target distance). Figure (a) compares the dose profile of a single microbeam scored between and 2 cm depth (in water) with and without beam divergence (Diverge and On Phantom, respectively). A ratio of the Diverge and On Phantom profiles is shown in figure (b) The effect of the multislit collimator. Figure (a) plots a ratio of the dose profile of a single microbeam obtained with and without the multislit collimator (MSC and NoMSC, respectively) and a point source (Pt src). A ratio of the corresponding MSC and NoMSC profiles obtained with a distributed source (Dist src) is plotted in figure (b). All dose profiles were scored between and 2 cm depth in water The effect of the source model. Figure (a) compares the dose profile of a single microbeam obtained with a point source (Pt src) to that produced by a distributed source (Dist src), using the multislit collimator (MSC). The dose profiles were scored between and 2 cm depth (in water), where a ratio of the profiles is plotted in figure (b) xvi

19 7.7 The effect of the multislit collimator (MSC) lateral offset. Figures (a) and (b) compare the dose profile of the central microbeam (C single) with those obtained for the 5th and 2th microbeams to the left and right of centre, respectively (i.e. in LHS array and RHS array) The effect of the multislit collimator (MSC) lateral offset. Figures (c) and (d) compare the dose profiles of the 5th and 2th microbeams on either side of centre, respectively (i.e. L5 single with R5 single and L2 single with R2 single) The effect of the simulation model. Figure (a) compares the dose profile of the central microbeam simulated with the single-beam and full array models (C single and C full, respectively) and scored between and 2 cm depth in water. A ratio of these C profiles, and those obtained for the L2 and R2 microbeams at either edge of the array, are shown in figure (b) Effect of the simulation model. Figure (a) shows the dose profile of a single microbeam used by the superposition model. Figure (b) plots the dose profile of the sup and full arrays obtained with the superposition and full array models, respectively, where a ratio of these profiles is shown in figure (c). All profiles were scored between and 2 cm depth (in water) The effect of the simulation model. Figure (a) plots a ratio of the sup and full array dose profiles of the L2 and R2 microbeams at the left and right edges of the array, respectively. Figure (b) compares the central microbeam profile in the full array (C full) with those at the left and right edges of the array (L2 full and R2 full, respectively) The effect of the simulation model. Figure (a) compares the PVDRs of microbeams in the sup array and full array. A ratio of the peak and valley doses and PVDRs of microbeams in the sup and full arrays is plotted in figure (b) The effect of the multislit collimator alignment on the dose profile of an array of 25 microbeams. Figures (a), (b), and (c) compare the dose profile of the full array with and without collimator rotations of ±0.05, ±0., and ±0.2 respectively The effect of the multislit collimator alignment on the dose profile of the central microbeam. Figures (a), (b), and (c) compare the dose profile of the central microbeam (C) produced with and without collimator rotations of ±0.05, ±0., and ±0.2 respectively The effect of positive angles of collimator rotation on the dose profiles of microbeams. Figures (a), (b), and (c) compare the dose profile of the central microbeam (C full) with those at the left and right edges of the array (L2 full and R2 full) for collimator rotations of 0.05, 0., and 0.2 respectively The effect of negative angles of collimator rotation on the dose profiles of microbeams. Figures (a), (b), and (c) compare the dose profile of the central microbeam (C full) with those at the left and right edges of the array (L2 full and R2 full) for collimator rotations of -0.05, -0., and -0.2 respectively xvii

20 7.6 The effect of the multislit collimator alignment on the peak and valley doses of microbeams. Figures (a) and (b) respectively compare the peak and valley doses of a microbeam array (normalised to dose in the central microbeam) with and without collimator rotations of ±0.05, ±0., and 0.2. The dose profile obtained with a -0.2 rotation is not shown owing to poor statistics The effect of the multislit collimator alignment on the PVDRs of microbeams. Figure (a) compares the PVDRs of a microbeam array obtained with collimator rotations of ±0.05, ±0., and ±0.2. A ratio of the PVDRs with and without collimator rotation is plotted in figure (b) The effect of the multislit collimator design on microbeam profiles. Figure (a) compares the dose profile of the central microbeam produced with the dual stack collimator (C full) with those at the left and right edges of array (L2 full and R2 full). The corresponding microbeam profiles obtained with a single stack collimator are shown in figure (b) Effect of the alignment of the single stack collimator on the dose profiles of microbeams. Figures (a) and (b) plot the dose profiles of the central microbeam (C full) and the L2 full and R2 full microbeams (at the left and right edges of the array) produced with the single stack collimator rotated through 0.05 and -0.05, respectively Effect of the interaction medium on microbeam profiles. Figure (a) compares the dose profile of the central peak in an array of 25 microbeams (C full) scored between and 2 cm depth in water (H 2 O) and polymethyl methacrylate (PMMA). A ratio of the dose profiles is shown in figure (b) Single microbeam profile showing the dose distribution according to the type of initial photon interaction in water (H 2 O) and polymethyl methacrylate (PMMA) for a 00 kev beam, where CS = Compton scattering, PE = Photoelectric effect, and Total = contributions from CS, PE, and Rayleigh scattering Effect of the height of scoring regions on the valley dose of microbeams. Comparison of the valley dose of the central microbeam (C full) in five lateral slices (each 0.2 cm high) to the total valley dose in all slices (i.e. 0 to cm) Effect of the height of scoring regions on the PVDR of microbeams. A ratio of the PVDR in five individual lateral slices (each 0.2 cm high) to the total PVDR integrated over all slices (i.e. 0 to cm) A.24 Circuit diagram of the pulse time delay. Discharge of the capacitor bank was initiated with a trigger signal generated from either a manual trigger button on the control panel or by an external transistor-transistor logic (TTL) input pulse A.25 Circuit diagram of current pulser. When a current of 200 A was pulsed through the coil, a magnetic field of about 2.5 T was estimated at the centre of the coil s air core A.26 Test results for the magnet coil. Charging the capacitor bank to 300 V enabled a discharge current of around 200 A to be pulsed through the coil. This corresponded to a peak flux of.3 T at the centre of the coil s surface xviii

21 PUBLICATION LIST The following publications are by the author, several of which are used in this work:. H. Nettelbeck, G. J. Takacs, M. L. F. Lerch and A. B. Rosenfeld, Microbeam radiation therapy: A Monte Carlo study of the influence of the source, multislit collimator and beam divergence on microbeams, Medical Physics, vol. 36(2), pp , H. Nettelbeck, G. J. Takacs and A. B. Rosenfeld, Effect of transverse magnetic fields on dose distribution and RBE of photon beams: comparing PENELOPE and EGS4 Monte Carlo codes, Physics in Medicine and Biology, vol. 53, pp , E. A. Siegbahn, H. Nettelbeck, E. Bräuer-Krisch, M. L. F. Lerch, A. B. Rosenfeld and A. Bravin, MOSFET dosimetry with high spatial resolution in intense synchrotron-generated x-ray microbeams, Medical Physics, vol. 36(4), pp , A. B. Rosenfeld, E. A. Siegbahn, E. Bräuer-Krish, A. Holmes-Siedle, M. L. F. Lerch, A. Bravin, I. M. Cornelius, G. J. Takacs, N. Painuly, H. Nettelbeck and T. Kron, Edge-on face-to-face MOSFET for synchrotron microbeam dosimetry: MC modeling, IEEE Transactions on Nuclear Science, vol. 52(6), pp , Dec H. Nettelbeck, M. Lerch, G. Takacs and A. Rosenfeld, Magneto-Radiotherapy: Making the electrons conform, Australasian Physical & Engineering Sciences in Medicine, vol. 3(), pp , Mar xix

22 6. H. Nettelbeck, M. Lerch, G. Takacs and A. Rosenfeld, Magneto-Radiotherapy: Using magnetic fields to guide dose-deposition, Australasian Physical & Engineering Sciences in Medicine, vol. 29(4), p. 359, Dec H. Nettelbeck, A. Rosenfeld, G. Takacs and M. Lerch, Magneto-Radiotherapy: Effect of magnetic field on dose distribution and RBE, Australasian Physical & Engineering Sciences in Medicine, vol. 28(4), pp , Dec H. Nettelbeck, M. Lerch, G. Takacs and A. Rosenfeld, Microbeam Radiation Therapy (MRT): Monte Carlo modelling of microbeams, Australasian Physical & Engineering Sciences in Medicine, accepted for publication. xx

23 CONFERENCES The author has presented work at the following conferences:. Australasian College of Physical Scientists and Engineers in Medicine symposium (MedPhys08), Sydney, Australia, Dec Presentation: Microbeam Radiation Therapy (MRT): Monte Carlo modelling of microbeams. 2. Australasian High Energy Physics and Medical Physics conference (AUSHEP08), Adelaide, Australia, Dec Presentation: Microbeam Radiation Therapy: Application of magnetic fields and the accuracy of Monte Carlo in MRT. 3. New Prospects for Brain Tumour Radiotherapy: Synchrotron Light and Microbeam Radiation Therapy conference (SYRAD 2008), European Synchrotron Radiation Facility (ESRF), Grenoble, France, June 2-4, Presentation: Modelling the source and multislit collimator geometry and their influence on MRT microbeam profiles. 4. Australasian College of Physical Scientists and Engineers in Medicine symposium (MedPhys07), Sydney, Aust., Dec Presentation: Magneto-Radiotherapy: Making the electrons conform. 5. Engineering and Physical Sciences in Medicine (EPSM06), Noosa, Australia, Sep. 7-2, Presentation: Magneto-Radiotherapy: Using magnetic fields to guide dose-deposition. 6. Australasian College of Physical Scientists and Engineers in Medicine symposium (MedPhys06), Sydney, Aust., Dec Presentation: Magneto-Radiotherapy: Using magnetic fields to guide dose-deposition. xxi

24 7. Australian Institute of Nuclear Science and Engineering 8th Radiation Biology conference (AINSE Radiation 2006), Sydney, Australia, April 20-2, Presentation: Magneto-Radiotherapy: Effect of a magnetic field on dose-deposition and RBE. 8. World Congress on Medical Physics and Biomedical Engineering 2006 (WC 2006), Seoul, Korea, Aug Sep. Magneto-Radiotherapy: effect of magnetic field on dose distribution (presented by A. B. Rosenfeld on author s behalf). 9. Engineering and Physical Sciences in Medicine (EPSM05), Adelaide, Australia, Oct , Presentation: Magneto-Radiotherapy: Effect of a magnetic field on dose-deposition and RBE. 0. Australian Experimental High Energy Physics Consortium (AEHEPC05), Melbourne, Australia, Dec. 2-4, Presentation: Magneto-Radiotherapy: Enhancement of dose distribution in radiotherapy and synchrotron MRT.. Experimental Radiation Oncology workshop (ERO 2004), Newcastle, Australia, Dec Presentation: Magneto-Radiotherapy: Effect of a magnetic Field on physical absorbed dose distribution and RBE. xxii

25 CHAPTER INTRODUCTION. Background and motivation The prevalence of cancer worldwide continues to drive scientists to search for a cure. While this thesis makes no attempt at finding a cure, it does constitute another step towards the research and development of current radiotherapy techniques for improving cancer treatment. Cancer is a group of diseases characterised by the uncontrolled growth and spread of abnormal cells. It is a leading cause of death worldwide, with 7.9 million deaths being attributed to it in 2007 []. Globally, over 22 million people are burdened by the disease which impinges on the lives of tens of millions every year [2]. In Australia, in 3 men and in 4 women will be diagnosed with cancer before the age of 75 [3]. Of the people who develop cancer, about one half will undergo some form of radiation treatment [2, 4]. Radiation therapy, or radiotherapy, is the medical use of ionising radiation to treat a variety of diseases. The ultimate goal of radiotherapy is to deliver a high dose of radiation to a well-defined target volume with minimal radiation toxicity to surrounding healthy tissues. Radiotherapy can be administered curatively for eradication of the disease, or palliatively for localised tumour control or symptomatic relief to prolong and improve the quality of life. Treatment can be delivered from outside the body via external beam radiotherapy, or from inside the body via brachytherapy (i.e. sealed sources are placed inside or close to the tumour) or systemic radiation (i.e. unsealed sources ingested or injected into the body). The type of radiation and dose delivery technique depends on the tumour type as well as its progression and location within the body (e.g. deep-seated tumours benefit from deep-penetrating radiation, whilst short-range radiation is suitable

26 2 for tumours that are localised or near to radiation-sensitive tissue). Today radiotherapy is used to treat most types of solid tumours such as cancer of the bladder, brain, breast, cervix, larynx, lung, prostate, skin, soft tissue, spine, stomach, and uterus. Over the last century, following the discovery of X-rays by Wilhelm Röntgen in 895 and shortly afterwards natural radioactivity by Henry Becquerel, the discipline of radiotherapy has progressed from experimental application of X-rays with rudimentary equipment to more accurate and efficient treatment procedures that use sophisticated technologies. Radiotherapy began towards the close of the 9th century, within two months of Röntgen s discovery of X-rays. It was pioneered by Emil Grubbé when he used X-rays to irradiate a patient with advanced breast cancer [5]. A couple of years later, in 898, Marie Curie s discovery of radium as a natural source of high-energy X-rays (i.e. γ-rays) led to its use in the treatment of deep-seated tumours [6]. By 90, the use of brachytherapy emerged with the implantation of radium tubes directly into the diseased region of the body. In 93, William Coolidge s invention of the hot-cathode tube (to thermally emit electrons) revolutionised radiotherapy in that it allowed the control of radiation quality and quantity (dose) [7]. During the 940s, with the introduction of particle accelerators and the betatron, megavoltage X-ray treatment became available for deep-seated tumours. Less than a decade later, the first clinical linear accelerator (linac) was built [8] and, in 953, the first patient treatment was recorded [9]. The availability of computers in the early 960s paved the way for a new era in cancer therapy and diagnosis. In the late 970s treatment planning profited enormously with the development of diagnostic imaging technologies such as computerised tomography (CT) and, less than a decade later, magnetic resonance imaging (MRI). This technology, which provides detailed patient-specific anatomical data, has enabled the determination of the size and location of the tumour as well as any nearby radiation-sensitive healthy tissues. Treatment planning uses this data to optimise the size and direction of radiation beams in such a way to maximise dose to the tumour while minimising the damage to surrounding healthy tissues.

27 3 Over the years, numerous 3-D dose-calculation algorithms have been developed for treatment planning in radiotherapy. Generally, these algorithms can be classified into two groups; i) analytical correction-based methods, which predict dose deposition using data collected in water, and ii) model-based methods, which use the physical principles of photon and electron transport to simulate patient treatment [0]. The primary difference between the two is that model-based methods do not rely on measured dose data to correct patient treatment []. Of these algorithms, those based on Monte Carlo modelling are considered to be the most accurate [0, 2 4]. Its superior accuracy over other dose calculation algorithms stems from its ability to model complex radiation transport in heterogeneous geometries for any incident beam, where the selection of particle positions and interaction types is made using random numbers. Monte Carlo also has the ability to directly simulate particle transport through the geometry of beam delivery devices, such as those in the treatment-head of a linac. It can also be used to estimate dose quantities from individual particle types and sources that are difficult or not amenable to measurement [3]. These abilities, coupled with increased computer processing power, have led to Monte Carlo becoming increasingly available in commercial radiation therapy planning systems. There is no universal method of cancer treatment. Although conventional external beam radiotherapy is one of the most common modalities, it can be unsuitable for some types of tumours. Studies have shown that broad-beam conventional radiotherapy treatment of infantile brain tumours can be irremediably damaging to the developing brain, especially for children less than three years of age [5 9]. Considering brain tumours are among the most common forms of cancer in children [7], a safe alternative treatment method is desirable. Microbeam Radiation Therapy (MRT) is a promising alternative. MRT is an innovative experimental technique that uses a synchrotron and multislit collimator to produce an array of parallel, rectangular, micron-sized X-ray beams (microbeams) [9 28] analogous to the parallel panels of open vertical blinds. Aimed at the tumour volume, the microbeams interact in tissue, delivering a lethal radiation dose

28 4 to cells in their path (i.e. peak regions) whilst sparing cells lying in the fraction of a millimeter spacing between adjacent microbeams, called valley regions. The advantage of MRT over broad-beam radiotherapy is the ability of normal tissue to tolerate large amounts of radiation in small volumes whilst preserving the tissue s architecture, which has been demonstrated in a number of small-animal MRT studies [8, 20, 2, 24, 28 30]. This high resistivity of normal tissue to radiation damage from microscopically thin ionising radiation beams was first observed by Curtis at the Brookhaven National Laboratory (BNL), in 967, when investigating the hazards of cosmic radiation on astronauts [3]. Almost 40 years later, the development of MRT began at the National Synchrotron Light Source (NSLS) in Upton, New York, USA [32] and a few years later at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. Today, MRT is in its final stages of development. At the ESRF, preparations are in place for clinical MRT trials on dogs which, if successful, could lead to the availability of MRT to humans..2 Objectives and scope of this research A primary objective of this thesis is to explore the potential therapeutic benefits that may arise with the application of magnetic fields during external photon beam and Microbeam Radiation Therapy (MRT) treatments. This work is based on the premise that magnetic fields can alter the trajectory of charged particles and the distribution of their dose. In radiobiology, or the study of ionising radiation on biological systems, the principle target for radiation-induced biological effects is the DNA of cells. Strand breaks in DNA from charged particle tracks and chemical species (free-radicals) can bring about cell death, carcinogenesis and mutation [33 35]. Successful cell-killing occurs when a sufficient number of breaks in the DNA occur within close proximity. This begs the question of whether magnetic fields can be used to alter the paths of charged particles (electrons) in such a way to bring about a change in their relative biological effectiveness. The influence of a magnetic field on the electron spectrum of a clinical 5 MV photon beam,

29 5 typically used in conventional external beam radiotherapy, will be discussed. The use of magnetic fields in radiotherapy, or magneto-radiotherapy, will also be investigated for MRT with the aim of improving the peak-to-valley dose ratio (PVDR) by reducing the lateral scatter of electrons out of the peak regions and into the valleys. This will be investigated with a combination of Monte Carlo simulation and physical measurement. Since the advent of MRT, there has been an ongoing quest to find a radiation detector suitable for measuring dose in micrometer-sized volumes. The MOSFET detector has shown potential with its small sensitive volume and micron resolution. Measurements will be performed to characterise the radiation response of the MOSFET for multiple use in MRT. Its ability to measure the lateral dose profiles of monoenergetic and polyenergetic microbeams, and hence estimate PVDRs, will also be investigated. An ongoing challenge in MRT is the resolution of discrepancies between the absorbed dose calculated by Monte Carlo and that measured experimentally. The need to resolve these discrepancies is driven by the desirability of making MRT available to humans, and hence the demand for an accurate dose planning system. This work addresses the importance of modelling beamline components by using PENELOPE Monte Carlo simulation to investigate the influence of the source, multislit collimator, and beam divergence on the dose profiles of microbeams..3 Thesis outline Monte Carlo simulation is used extensively throughout this thesis for the calculation of dose and other physical quantities that may be difficult or not amenable to measurement. An introduction to the Monte Carlo method and a description of the Monte Carlo PENELOPE toolkit are provided in chapter 2. Chapter 3 uses Monte Carlo PENELOPE to explore the influence of a transverse magnetic field on the dose distribution of high-energy photon beams, such as those typically used in radiotherapy. A comparative study is made between the dose distributions

30 6 obtained with the Monte Carlo PENELOPE and EGS4 codes for the purpose of benchmarking PENELOPE s charged particle transport algorithm in static electromagnetic field applications. The optimal width of the magnetic field and depth at which it is applied to achieve maximum therapeutic benefit is also presented. Chapter 4 extends this work by investigating potential changes in the relative biological effectiveness from the redistribution of electrons in a transverse magnetic field. Chapter 5 investigates the performance of edge-on MOSFET dosimeters for use in MRT at the European Synchrotron Radiation Facility in Grenoble, France. A study of the MOSFET s radiation response and ability to measure the dose profiles of monoenergetic and polyenergetic microbeams with micron-sized resolution is presented. The measured dose profiles and PVDRs of microbeams are supplemented with theoretical results obtained by the means of Monte Carlo PENELOPE simulation. Chapter 6 explores the potential use of magnetic fields in MRT to alter the electron distribution, and hence, the PVDR of microbeams. This is investigated for transverse and longitudinal magnetic fields using a combination of Monte Carlo simulations and physical experiments, with three different magnet devices. Chapter 7 addresses the importance of accurately modelling beam delivery and microbeam transport in MRT by challenging simplifications commonly made in Monte Carlo studies. Simulations with the Monte Carlo PENELOPE code are used to investigate the influence of the source, multislit collimator and beam divergence (from the source to detector) on the dose profiles and PVDRs of microbeams. Also investigated is the effect of the collimator alignment, height of scoring bins, and type of interaction medium. A comparison of the dose profile of a microbeam array obtained with a full model of the beamline to that generated from the superposition of a single microbeam profile is also presented.

31 CHAPTER 2 RADIATION TRANSPORT AND THE MONTE CARLO PENELOPE CODE This chapter provides a review of the different principles of radiation transport in matter. It concentrates on photon and electron transport, as the bulk of this thesis is concerned with photon beam irradiation. The implementation of radiation transport in Monte Carlo is also discussed for the PENELOPE toolkit, which was used extensively in this work. 2. Interactions of radiation with matter 2.. Photon interactions When a photon traverses a medium, it undergoes interactions with the atomic nuclei and electrons that comprise the medium. A primary photon is the term used to describe a photon which has not interacted with the medium. When such a photon undergoes an interaction it is referred to as a scattered photon. The probability of primary or scattered photon interactions depends on the energy of the photon and the composition of the medium with which it interacts. The dominant photon interaction processes; coherent (Rayleigh) scattering, incoherent (Compton) scattering, photoelectric absorption and electron-positron pair production, are outlined below. Figure 2. shows the cross sections for photon interactions in water, where Compton scattering can be seen to dominate between about 30 kev and several MeV, which is the energy range of most photons in this study. Interaction cross section data extracted from the National Institute of Standards and Technology (NIST) XCOM Photon Cross Sections database [36] 7

32 P l e a s e s e e p r i n t c o p y f Figure 2.: Cross sections for photon interactions in water. Data extracted from the NIST oxcom Photon Cross Sections database [36]. r i m a g e 2... Coherent (Rayleigh) scattering Please see print copy for image Coherent or Rayleigh scattering is the process by which a photon interacts with atomic electrons but does not excite or ionise the target atom. While the direction of the photon may change, resulting in a transfer of momentum to the atom, the energy of the photon remains the same. A coherent scattering event can be described by considering the photon as an electromagnetic wave. The incident wave causes the atomic electrons to oscillate with the same frequency and in phase with one another, resulting in the interference of electromagnetic waves scattered from different parts of the atomic-charge cloud. Thus, the scattered photon emerges with the same frequency (energy) but different direction of motion. From the conservation of energy and momentum, the photon is predominantly scattered in the forward direction. Rayleigh scattering mainly occurs at low photon energies for large Z values. In water, it is important at photon energies below about 0 kev (refer to figure 2.). The cross section for this process, dσ Ra /dθ, is given by Please see print copy for image Please see print copy for image

33 9 dσ Ra dθ = r2 o 2 ( + cos2 θ)[f (x, Z)] 2 2πsinθ (2.) where r o is the classical electron radius, θ is the scattering angle, x is the magnitude of momentum transfer in the collision (x = (sinθ/2)/λ), Z is the atomic number of the target atom, and F(x,Z) is called the atomic form factor [37]. This factor is a monotonically decreasing function of the momentum transfer, where F(x,Z) approaches Z for a small θ value, while for a large θ value it tends toward zero. For low photon energies and small momentum transfers, the cross section for Rayleigh scattering, dσ Ra, can be approximated by [38] dσ Ra 8 3 πr2 oz 2 (2.2) Incoherent (Compton) scattering Compton scattering is the predominant mode of photon interaction in water and soft tissue between energies of about 30 kev and 2 MeV (refer to figure 2.). In Compton scattering, the incident photon collides inelastically with an atomic electron. As a result, some of the photon energy, hv, is scattered and some is transferred to the electron as kinetic energy, E k. By conservation of energy, assuming the electron is free or unbound (as the binding energies are a small fraction of the photon energy), the scattered photon will retain an energy hν = hν - E k. Applying conservation of momentum leads to the following relation between the energy of the scattered photon and its scattering angle, θ, hν = hν ( ) hν + m oc ( cosθ) 2 (2.3) where h is Planck s constant, ν is the photon frequency, m o is the electron rest mass and c is the speed of light.

34 0 This equation shows that the maximum energy transferred to an electron is when the incident photon makes a direct hit with the electron and is scattered through 80 o (i.e. back along its incoming path). In this case, the electron will travel forward in the direction of the incident photon (θ = 0). In such a collision, the scattered photon will retain its minimum energy. However, when a photon instead makes a grazing hit with the electron, it scatters in the forward direction (θ 0) while the electron is set in motion at almost 90 o. In this type of collision, the scattered photon retains a maximum energy (essentially the full incident photon energy) whilst the electron receives almost no energy. Collisions between these two extremes are possible. The differential cross section for a photon interacting with a free electron at rest is given by the Klein-Nishina equation: ( ) dσ E dω E + E E + cos2 ϕ (2.4) where E is the energy of the scattered photon given by E = E + [E/(m o c 2 )]( cosϕ) (2.5) The angle of the Compton electron, φ e, is therefore defined as cotφ e = ( + E ) tan( ϕ m o c 2 2 ) (2.6) Figure 2.2 shows the angular distribution of Compton scattered photons of energies 0., 0.5,, 5, 0, and 5 MeV calculated from the Klein-Nishina cross section (equation 2.4). The corresponding angular distribution of Compton electrons (calculated from equation 2.6) is plotted in figure 2.3.

35 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Angular distribution of Compton scattered photons 90 o 20 o 60 o 50 o 30 o 80 o Differential cross section (σ/σ max ) 0 o Figure 2.2: Angular distribution of Compton scattered photons calculated from the Klein- Nishina cross section (equation 2.4). A plot of the intensity of a scattered photon of 0., 0.5,, 5, 0, and 5 MeV interacting with a free electron at the centre of the graph. Angular distribution of electrons from Compton scattered photons 0.MeV 90 o 0.5MeV MeV 20 o 60 o 5MeV 0MeV 5MeV 50 o 30 o 80 o Differential cross section (σ/σ max ) 0 o Figure 2.3: Angular distribution of Compton scattered electrons calculated from the Klein-Nishina cross section (equation 2.6). A plot of the intensity of the electrons produced from Compton scattered photons of 0., 0.5,, 5, 0, and 5 MeV.

36 Photoelectric absorption In the photoelectric process, a photon of energy hν is absorbed by an atom resulting in the ejection of a bound electron from one of the K, L, M, or N shells. The ejected electron receives almost all of the photon energy, emerging with a kinetic energy E k = hν - E s, where E s is the binding energy of the electron. Such an ionisation leaves the atom in an excited state. As the atom returns to the ground state it emits characteristic radiation, either as X-rays or Auger electrons, whose energy depends on the shell from which the electron was ejected. The probability of photoelectric interaction increases rapidly with decreasing energy, particularly for high Z materials, where it is the predominant mode of interaction at low photon energies. In water and soft tissue, this corresponds to photon energies below about 30 kev, as shown in figure 2.. Photoelectric interaction is most likely to occur with a K-shell electron (of the target atom), providing the photon energy is greater than the K-shell binding energy Electron-positron pair production For a pair production event to occur, the energy of the incident photon, hν, must be at least twice the rest mass energy of an electron (.022 MeV). In these interactions, a photon passes near the nucleus of an atom where its energy is converted to form an electron-positron pair. The excess energy of the photon (hν MeV) is shared between the electron and positron as kinetic energy. The electron and positron travel through matter ionising and exciting particles until they are brought to rest. When the positron nears the end of its path, it combines with an electron and they undergo annihilation to produce two 0.5 MeV photons which are emitted in opposite directions.

37 Electron interactions The interaction of photons with matter gives rise to secondary electrons. Unlike photons which lose their energy in a few collisions, electrons can undergo a very large number of collisions before all of their energy is absorbed. The types of interactions whereby electrons lose energy include collisions with atomic electrons (collision energy loss) and encounters with the Coulomb force of atomic nuclei (radiative energy loss). Both types of interactions are inelastic as they involve the loss of incident electron energy. Elastic interactions can occur when an electron passes by a nucleus at a large distance. In these types of Coulomb force interactions, the electron suffers a change in direction but no loss in kinetic energy since the mass of the electron is substantially smaller than that of the atom. In radiobiology, cell damage is primarily attributed to the processes of ionisation and excitation that result from collision energy loss [0]. Ionisation occurs when the incident electron strips the atom of a bound electron. Excitation is the process whereby the incident electron excites an atomic electron by temporarily elevating it to a higher energy level (which results in the emission of characteristic radiation). Both of these processes change the chemical reactivity of the molecule involved, thereby contributing to radiation damage. Most encounters involving collision energy losses result in small energy transfers between the incident and atomic electrons. However, it is also possible for large collision energy losses to occur when an incident electron transfers a higher proportion of its energy to an atomic electron. In this case, the electron that is knocked out of the atom will have sufficient energy to produce a track of its own. Such electrons are known as delta rays, or δ-rays. Radiative energy losses may occur when an electron passes very close to the nucleus of an atom, where the electromagnetic force sends the electron in a partial orbit around the positive nucleus. As a result, the electron recedes from the interaction with reduced energy. This loss in energy appears as a bremsstrahlung photon in order to conserve energy. The probability of such an interaction increases with increasing electron

38 4 energy and decreasing distance between the electron and the nucleus. It is also dependent on the density, or atomic number of the absorber atoms, where bremsstrahlung production is more prevalent in media of higher atomic number (i.e. lead) than in media of low atomic number (i.e. water or soft tissue), where energy loss is predominantly through ionisation events. 2.2 Monte Carlo PENELOPE code Monte Carlo is a numerical technique that uses a class of computational algorithms to solve complex physical and mathematical problems. It is based on the generation of random numbers which are used to sample values for the problem variables from known Probability Density Functions (PDF) [39, 40]. In the case of radiation transport in matter, a set of Differential Cross Sections (DCS) for the relevant interaction mechanisms are used to determine the PDFs of random variables that characterise a particle track [38]. These variables may be quantities such as the distance travelled between successive interaction events, the type of interaction and target particle, or the energy loss and angular deflection in an event (and the initial state of any secondary particles produced). Monte Carlo is therefore a popular theoretical tool used to evaluate radiation transport in complex target geometries and material compositions. The Monte Carlo PENELOPE code is a computational algorithm used for the simulation of coupled electron-photon transport [38]. The algorithm simulates different interaction mechanisms using a combination of numerical databases and analytical cross section models for particles with an energy between 00 ev and GeV Brief outline of code structure and operation The kernel of the code system is the FORTRAN 77 subroutine package PENE- LOPE [38]. It uses a collection of subprograms and relevant subroutines to simulate electron-photon showers in arbitrary material systems. Photon histories are simulated individually in chronological succession, while the generation of electron and positron

39 5 tracks are simulated using the mixed simulation method (discussed in section 2.2.2). Secondary particles generated with an initial energy above a specified absorption energy are stored on a secondary stack and simulated in chronological order following the completion of each primary track. The processes whereby secondary particles are emitted are described in section 2.. The PENELOPE subroutine is steered by a MAIN program written by the user for their particular problem. This program controls the evolution of particle tracks and scoring of relevant quantities (i.e. energy distribution within arbitrary geometries), leaving PENELOPE to do most of the simulation work. Physical information for each interaction medium (i.e. physical composition, interaction cross sections, relaxation data, etc) are read from material data files, which are extracted from the relevant atomic interaction databases. In the case of material systems with complex geometries, operations to determine the active medium and change it when the particle crosses into another one can be performed automatically by the subroutine package PENGEOM. For applications involving static external magnetic fields, PENELOPE uses a subroutine package PENFIELD, which is linked to PENELOPE and PENGEOM, to track particle transport in a given field and material configuration [38] Particle transport In PENELOPE, photon transport is simulated individually (i.e. event by event). Electron and positron transport, on the other hand, are described by means of mixed simulation procedures [4]. This is because individual simulation of electron or positron transport may be infeasible owing to the large number of interactions that these particles can experience. The mixed simulation method therefore combines the individual simulation of hard collisions (i.e. events with scattering angle θ or energy loss W larger than preselected cutoff values θ c and W c ) with grouped simulation of multiple soft collisions (i.e. events where θ < θ c or W < W c ). Hard collisions are simulated with the appropriate

40 6 DCSs, while multiple soft collisions along a step of the particle s path (between two consecutive hard events) are simulated in a single artificial soft scattering event by means of the random hinge method [4]. In this case, the simulation detail is dependent on the user defined parameters C and C 2. The average angular deflection is related to C such that C - cosθ, and the maximum average fractional energy loss in a single step (i.e. along the mean free path between consecutive hard elastic events) is defined by C 2. For hard collisions, the cutoff energies for inelastic collisions and bremsstrahlung emission, W cc and W cr respectively, are defined by the user. The cross section data used by PENELOPE are obtained from a number of sources. For photoelectric absorption and pair production (ranging from 00 ev to GeV), the DCSs are sourced from the Evaluated Photon Data Library (EPDL) database [42] and the XCOM Photon Cross Sections program [43], respectively. The DCSs for Compton scattering events are described by means of the relativistic impulse approximation [44], and the transition probabilities for atomic relaxation events (i.e. emission of characteristic radiation and Auger electrons) from vacancies produced in the K-shell and L-subshells are extracted from the Evaluated Atomic Data Library (EADL) [45]. In the case of elastic electron scattering, the DCSs are derived from a modified Wentzel distribution with parameters obtained from relativistic partial-wave analysis [38]. Note that for low energy photons below the K absorption edge, the reduced form of the Rayleigh scattering cross section (equation 2.2) does not incorporate anomalous scattering factors [46, 47] that would otherwise lead to a general reduction in the cross section [38] Electron transport in magnetic fields Radiation transport in static uniform magnetic fields is implemented in PENELOPE by the means of a robust tracking algorithm [38]. When a charged particle interacts in a static external magnetic field its loss in kinetic energy and change in direction of motion are determined by the means of this tracking algorithm. In the absence of a magnetic field, an electron will move in a straight line between consecutive interaction events.

41 7 In the presence of a magnetic field, however, this straight trajectory segment will be divided into macroscopic lengths (of maximum allowed step length) to account for the effect of the magnetic force. In such simulations, the accuracy of generated trajectories is controlled by the smallness of the user-defined delta simulation parameters δ B, δ E and δ v (i.e. relative changes in magnetic field, kinetic energy and velocity, and direction of motion respectively). In the case of a uniform magnetic field, the tracking algorithm is exact and independent of step length.

42 8

43 CHAPTER 3 INFLUENCE OF A TRANSVERSE MAGNETIC FIELD ON THE DOSE DISTRIBUTION IN PHOTON BEAM RADIOTHERAPY 3. Introduction In this chapter, the influence of a transverse magnetic field on the dose distribution of photon beams is investigated with Monte Carlo PENELOPE simulation. A comparison is made between the dose distributions obtained with Monte Carlo PENELOPE and EGS4 codes in order to benchmark the performance of PENELOPE s charged particle transport algorithm in applications involving static electromagnetic fields. The optimal width of magnetic field and the depth at which it is applied to achieve maximum therapeutic benefit is also investigated. Many of the results appearing in this chapter have been published previously in a peer-reviewed journal article [48]. Since the advent of radiotherapy as a means of tumour control an ongoing challenge has been to reduce the radiation dose delivered to normal tissue. Conformal radiotherapy, intensity modulated radiotherapy, and brachytherapy are three methods in current use. Magneto-radiotherapy, or the use of magnetic fields to produce a favourable redistribution of dose, despite being suggested over half a century ago, is still not in use. This is primarily due to the practical difficulty of applying magnetic fields of sufficient strength to bring about a significant alteration of the dose deposition. A secondary consideration is the incorporation of the effects of the magnetic fields on the dose distribution into the treatment planning process. A third consideration is the potential for any change in radiobiological effectiveness of the radiation through physical, chemical, or biological means. Changes in technology mean that the ability to apply sufficiently strong magnetic 9

44 20 fields will soon be at hand. Therefore it is desirable to extend earlier studies to allow further progress to be made in the second and third areas referred to above. The work in both the current and succeeding chapters constitutes another step on that path. The concept of applying magnetic fields to alter the dose deposition of scattered electrons from radiotherapy beams was suggested by Bostick in 950. He proposed that a longitudinal magnetic field applied during electron beam therapy would reduce the lateral scattering of secondary electrons, thereby reducing the penumbral broadening of the beam with depth [49]. Since then a number of Monte Carlo studies have investigated the potential for transverse and longitudinal magnetic fields to alter the dose distribution from radiotherapy beams [50 63]. An electron travelling in a magnetic field experiences a Lorentz-force which bends its trajectory, between scattering events, into a helical-shaped path (the entire trajectory will not be a perfect helical shape due to scattering). The radius of curvature of an electron, R e, depends on the electron s kinetic energy, E k, and the strength of the external magnetic field, B, in which it is travelling. This dependence is given by R e = M ec eb (Ek E o ) 2 + 2E k E o (3.) where M e, e, and E o are the mass, charge, and rest energy of an electron respectively, and c is the speed of light. The mean free path of an electron between scattering events is also strongly energy dependent. This is shown in figure 3. with a plot of the mean free path of an electron (in water) and its radius of curvature when subject to a, 2, 5 and 20 T magnetic field. Naively, one might expect to see an effect of the magnetic field on the dose deposition only if these two characteristic lengths are comparable in size. We will see later that an effect exists even when the radius of curvature is orders of magnitude larger than the mean free path. This occurs because of the large number of interactions that an electron needs to undergo before its trajectory is significantly altered.

45 2 Also shown in the figure is the range of an electron in water as a function of energy. A magnetic field will influence an electron s trajectory when this distance is larger than or comparable with its radius of curvature. For a T magnetic field, this is satisfied by electrons with an energy of MeV and above. For electrons below MeV, these distances become comparable at stronger magnetic fields (e.g. 00 T for 0.0 MeV electrons). Distance (cm) Electron range, radius of curvature, and mean free path in water electron range e-05 mean free path T radius of curvature e-06 2T radius of curvature e-07 5T radius of curvature 20T radius of curvature e e+06 e+07 e+08 Energy (ev) Figure 3.: Energy dependence of the range, mean free path, and radius of curvature of an electron moving in magnetic field. The range of an electron (in water) as a function of energy is based on the data in table 3.. Studies concentrating on the alteration of dose deposition with a transverse magnetic field (i.e. perpendicular to beam direction) began in 975 with a Monte Carlo study by Shih [50]. They found that a 6 T transverse magnetic field applied to a 70 MeV electron beam reduced the lateral spread of electrons, forming a localised maximum dose region at the end of their range analogous to the well-known Bragg peak. Since then, a number of studies have investigated the dose redistribution obtained with transverse magnetic fields applied to radiotherapy beams. Whitmire and Bernard [5, 52] measured surface dose reductions of up to 40% in polystyrene and cork phantoms when magnetic fields of 0.9 to.8 T were applied to betatron accelerator energies of 0-45 MeV. A Monte

46 22 Table 3.: Range of electrons in water as a function of energy [37]. Energy (MeV) Range (cm) Carlo study by Nardi and Barnea [54] showed up to 50% reduction in the surface to peak dose (a ratio used to monitor skin sparing) with a 3 T uniform field applied to a 5 MeV electron beam beyond 4 cm depth (in tissue). A later Monte Carlo study by Lee and Ma [57] also found transverse magnetic fields applied to electron beams to significantly reduce the surface to peak dose and cause steeper dose fall-offs in the maximum dose. Fewer studies have investigated the effect of a magnetic field on the dose distribution from photon beams. Recognising this gap in the literature, Jette performed Monte Carlo simulations to study changes in the dose distribution for 5, 30, and 45 MV photon beams when non-uniform transverse magnetic fields of up to 5 T (central strength) were applied [56]. For all three beams, a 2 T field produced a significant enhancement in the maximum dose and a slightly larger enhancement with 3 T, where these regions of dose enhancement were immediately followed by a region of dose reduction. A further enhancement in the maximum dose with stronger magnetic fields was only observed with the 45 MV beam. Localised regions of dose enhancement and dose reduction were also observed by Li et al. in a Monte Carlo study with EGS4 investigating the effect of transverse magnetic fields on the dose distribution from photon beams, using different strength magnetic fields ( to 20 T) and photon beam energies (Co 60, 6, 0, 5, 24, and 50 MV) [58]. The

47 23 slice of uniform transverse magnetic field was applied between 7 and 9 cm depth in a water phantom, and zero magnetic field was applied to the remainder of the volume. The application of different strength magnetic fields to a 5 MV beam produced dose enhancements and dose reductions of up to 97% and 79% respectively (these were obtained with a 5 T magnetic field). Li et al. also studied the effect of photon beam energy on the dose distribution of Co 60, 6, 0, 5, 24, and 50 MV photon beams with a 5 T magnetic field and observed an increase in the maximum dose and a reduction in the minimum dose when the beam energy was increased. Li et al. quantifies this dose perturbation effect by calculating a Dose Perturbation Factor (DPF) which is a ratio of dose obtained with magnetic field to that obtained without magnetic field as a function of depth along the axis of the beam. Hence, a DPF <.0 is a dose reduction, while a DPF >.0 is a dose enhancement. Localised regions of dose enhancement and dose reduction could benefit the treatment of tumours near radiation-sensitive structures by aligning the region of dose enhancement with the tumour volume and the region of dose reduction with the critical structure. This is shown in figure 3.2 with Monte Carlo PENELOPE simulation of the effect on the depth-dose and DPF of a 0 MV beam when a slice of 5 T transverse magnetic field, B, is applied between 7 and 9 cm depth (in water). 3.2 Simulation methods The accurate low-energy electron and photon cross sections gives PENELOPE a superiority over other Monte Carlo codes for applications involving low-energy transport. For example, PENELOPE can transport electrons and photons with energies as low as 00 ev [38] which is much lower than the EGS4 transport cutoff of kev for photons and tens of kev for charged particles [64]. Another key difference between EGS4 and PENELOPE lies in the electron transport algorithms. While both codes use exact tracking algorithms for charged particle transport in a magnetic field, the implementation of their

48 24 Effect of magnetic field on 0MV depth-dose curve Energy (ev) / primary photon (a) B=0 B B=0 B=zero B=5T Depth (cm) DPF for 0MV beam with 5T magnetic field.8 (b) DPF (B/B=0) B=0 B B= Depth (cm) Figure 3.2: Effect of a slice of 5 T transverse magnetic field (7 to 9 cm depth) on the: (a) depth-dose, and (b) dose perturbation factor (DPF) of a 0 MV beam (direction of magnetic field is out of the page).

49 25 condensed history methods varies significantly. Hence, it is logical to examine whether the two codes make similar predictions about the effect of a magnetic field on the dose deposition. This present work compares the dose enhancement and dose reduction obtained with Monte Carlo PENELOPE and EGS4 codes for different strength magnetic fields and photon beam energies, based on the EGS4 study by Li et al. [58] which used input energy spectra for the 6, 0, 5, 24 and 50 MV photon beams from Mohan et al. [65]. The photon beam was incident on a cm 3 (width height depth) water phantom with a 4 4 cm 2 field at 00 cm source to surface distance (SSD). A slice of uniform transverse magnetic field was applied between 7 and 9 cm depth in the phantom, and the remaining volume outside of this region was set to zero magnetic field. Cylindrical scoring bins of 0.5 cm radius 0.2 cm depth were used to tally the energy deposition from particle interactions. The electron and photon transport cutoffs were 0 kev and the total number of histories were 0 8 to ensure the relative uncertainty (98% confidence level) of energy deposition in each bin did not exceed 2%. PENELOPE simulations were carried out with identical combinations of magnetic field strength and photon beam energy as those used in the EGS4 study with the exception of the 50 MV beam (i.e. Co 60, 6, 0, 5, and 24 MV). The Mohan photon beam input spectra used in Monte Carlo simulation of the 6, 0, 5, and 24 MV beams is plotted in figures 3.3 (a), (b), (c) and (d), respectively. The PENELOPE simulation parameters, unless otherwise stated, were identical to those used in the EGS4 study (i.e. electron and photon energy cutoffs, number of histories, and bin volumes). Statistical uncertainties of three standard deviations were calculated for each bin. Due to a discrepancy with the EGS4 results for 5 MV and 2 T, the simulations were repeated using photon beam input spectra determined by Sheikh-Bagheri and Rogers [66] for 6, 0, and 5 MV beams (24 MV spectrum was not available) to compare with the DPFs obtained with the spectra of Mohan et al. [65].

50 (a) 6MV photon beam spectrum % Weight e+06 2e+06 3e+06 4e+06 5e+06 6e+06 Energy (ev) (b) 0MV photon beam spectrum % Weight e+06 4e+06 6e+06 8e+06 e+07 Energy (ev) Figure 3.3: Figure (a) and (b) show the input photon beam spectrum (based on the Mohan spectra [65]) used for simulations with 6 and 0 MV beams respectively.

51 27 % Weight MV photon beam spectrum (c) 0 3e+06 6e+06 9e+06.2e+07.5e+07 Energy (ev) (d) 24MV photon beam spectrum % Weight e+06 8e+06.2e+07.6e+07 2e e+07 Energy (ev) Figure 3.3: Figure (c) and (d) show the input photon beam spectrum (based on the Mohan spectra [65]) used for simulations with 5 and 24 MV beams respectively.

52 28 Further PENELOPE simulations were performed with twice the number of scoring bins (i.e. the bin depth was halved from 0.2 cm to 0. cm depth) to improve the DPF resolution, particularly around the magnetic field boundaries where the DPF rapidly increases or decreases. These simulations were performed with the Mohan et al. photon beam spectra and identical simulation parameters to those used above, apart from the smaller bin volume. In the course of comparing the PENELOPE and EGS4 dose distributions, a persistant discrepancy in one set of the results led to an investigation of the effect of PENE- LOPE elastic scattering parameters C and C 2 on the accuracy of the simulations. Limited to the interval of (0,0.2), Salvat et al. recommends setting C and C 2 to a conservative value of 0.05, indicating that using smaller values is at the expense of increased simulation time whilst larger values may reduce accuracy. In this study, the values of C and C 2 inside the region of magnetic field were both varied from 0.05 to a value of 0.02, 0., 0.2 and 0.5 (in regions beyond the magnetic field, C and C 2 remained at 0.05). The influence of electron and photon low-energy transport cutoffs on the DPF were also investigated for 2 and 5 T magnetic fields applied to a 5 MV beam. Simulations were also performed to study the dose distribution of a photon beam with the 2 cm slice of transverse magnetic field applied at different depths. This was investigated for a 5 MV photon beam and 5 T magnetic field at depths of 0 to 2 cm, 0.5 to 2.5 cm, 2 to 4 cm, 4 to 6 cm, and 7 to 9 cm in the water phantom. Investigations were also carried out to determine the optimal magnetic field thickness for producing maximum dose enhancements and reductions. Simulations were performed with transverse magnetic fields of 2, 5 and 0 T with thicknesses ranging from to 4 cm and applied to 6, 0, 5 and 24 MV photon beams. The width of each slice was centred at 8 cm depth in the water phantom.

53 Simulation results 3.3. Effect of the magnetic field strength The effect of magnetic field strength on a 5 MV beam is shown in figure 3.4 with a plot of the DPF as a function of depth along the central axis. Tables 3.2 and 3.3 compare the maximum and minimum DPFs obtained with PENELOPE and EGS4 (using identical bin volumes) for a 5 MV beam subjected to different magnetic fields, where PENELOPE(Mo) and PENELOPE(SBR) are the results obtained with Mohan et al. and Sheikh-Bagheri and Rogers spectra, respectively. Also included in the tables and figure 3.5 are the DPFs obtained with a 2 T field using different elastic scattering values C and C 2, demonstrating clearly that these have no effect on the results. The largest dose enhancement (9%) was obtained with a 5 T magnetic field, which was more than double that obtained with 2 T and 8 times larger than that obtained with T. Further increases in field strength failed to yield larger dose enhancements where values of 79%, 82%, and 80% were obtained with 0, 20, and 00 T respectively. Almost all of the PENELOPE DPF results were within 4% of those obtained with EGS4. The exceptions were the 2 T maximum DPF and the 2 and 20 T minimum DPFs, yielding respective discrepancies of 24%, 5%, and 0% for PENELOPE(Mo) and 24%, 4%, and 5% for PENELOPE(SBR). All PENELOPE(Mo) and PENELOPE(SBR) results were within 4% of each other. Reducing the PENELOPE electron and photon lowenergy transport cutoffs from 0 kev to kev had no effect on the DPFs of a 5 MV beam subjected to 2 and 5 T magnetic fields. Figure 3.4 shows the improved resolution in DPF with smaller bin volumes (0. cm instead of 0.2 cm depth), particularly in the dose enhancement and dose reduction regions at the magnetic field boundaries. A comparison of the maximum and minimum DPFs obtained with PENELOPE and EGS4 are presented in tables 3.4 and 3.5, where the results labelled PENELOPE(A) and PENELOPE(B) correspond to a bin depth of 0.2 cm (i.e. same bin volume as that used by EGS4 study) and 0. cm, respectively.

54 30 DPF (B/B=0) (a) Effect of magnetic field strength (0.2cm bin depths) B=0 B B= Depth (cm) B=T B=2T B=5T B=0T B=20T B=00T DPF (B/B=0) (b) Effect of magnetic field strength (0.cm bin depths) B=0 B B= Depth (cm) B=T B=2T B=5T B=0T B=20T B=00T Figure 3.4: Dose distribution of a 5 MV beam (in water) subjected to a slice of, 2, 5, 0, 20 and 00 T transverse magnetic field (7 to 9 cm depth), using bin depths of: (a) 0.2 cm, and (b) 0. cm.

55 3 Table 3.2: Comparison of the maximum DPF for a 5 MV beam with B = to 00 T. EGS4 PENELOPE(Mo) PENELOPE(SBR) B(T) DPF DPF Mo:EGS4 DPF SBR:EGS4 SBR:Mo.08. ± ± ± ± (C=0.02) -.4 ± (C=0.) -.40 ± (C=0.2) -.4 ± (C=0.5) -.4 ± ± ± ± ± ± ± ± ± ± ± ± Table 3.3: Comparison of the minimum DPF for a 5 MV beam with B = to 00 T. EGS4 PENELOPE(Mo) PENELOPE(SBR) B(T) DPF DPF Mo:EGS4 DPF SBR:EGS4 SBR:Mo ± ± ± ± (C=0.02) ± (C=0.) ± (C=0.2) ± (C=0.5) ± ± ± ± ± ± ± ± ± ± ± ± According to the ratio of PEN(B) to PEN(A), the maximum and minimum DPFs for the 0. cm bins are as much as % larger and 33% smaller than those obtained with 0.2 cm bins. This difference is attributed to the higher resolution of the smaller bins, particularly at the magnetic field boundaries where the dose gradients are steep.

56 32 DPF (B/B=0) Effect of elastic scattering parameters C and C 2 C=0.02 C=0.05 C=0.0 C=0.20 C= B=0 B=2T B= Depth (cm) Figure 3.5: Effect of the elastic scattering parameters C and C 2 (C = C = C 2 ) on the dose deposition of a 5 MV beam (in water) subjected to a 2 T transverse magnetic field (7 to 9 cm depth). Table 3.4: Comparison of the maximum DPF for a 5 MV beam with B = to 00 T using bin depths of 0. and 0.2 cm. EGS4 PENELOPE(A) (0.2cm bins) PENELOPE(B) (0.cm bins) B(T) DPF DPF PEN(A):EGS4 DPF PEN(B):EGS4 PEN(B):PEN(A)).08. ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

57 33 Table 3.5: Comparison of the minimum DPF for a 5 MV beam with B = to 00 T, and bin depths of 0. and 0.2 cm. EGS4 PENELOPE(A) (0.2cm bins) PENELOPE(B) (0.cm bins) B(T) DPF DPF PEN(A):EGS4 DPF PEN(B):EGS4 PEN(B):PEN(A) ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± Effect of the photon beam energy Figure 3.6 shows the dose perturbation obtained with a slice of 5 T transverse magnetic field (7 to 9 cm depth) applied to Co 60, 6, 0, 5, and 24 MV photon beams. Tables 3.6 and 3.7 compare the maximum and minimum DPFs obtained with PENELOPE and EGS4, where PENELOPE(Mo) and PENELOPE(SBR) are the results obtained with Mohan et al. spectra and Sheikh-Bagheri and Rogers spectra, respectively. The PENE- LOPE(Mo) maximum and minimum DPFs were within 6% of those obtained with EGS4. Apart from a 9% discrepancy between the 0 MV minimum DPFs, the PENELOPE(Mo) and PENELOPE(SBR) DPFs were within 5% of each other. Repeating the 0 MV simulations with different random seed values had no affect on the minimum DPF result. Table 3.6: Comparison of the maximum DPF for different photon beams with B = 5 T. EGS4 PENELOPE(Mo) PENELOPE(SBR) Beam DPF DPF DPF(Mo:EGS4) DPF DPF(SBR:EGS4) DPF(SBR:Mo) Co ± ± MV ± ± MV ± ± MV.97.9 ± ± MV ±

58 34 DPF (B/B=0) Effect of photon beam energy B=0 B=5T B= Depth (cm) Co60 6MV 0MV 5MV 24MV Figure 3.6: Dose distribution of Co 60, 6, 0, 5 and 24 MV photon beams (in water) subjected to a slice of 5 T transverse magnetic field (7 to 9 cm depth). Table 3.7: Comparison of the minimum DPF for different photon beams with B = 5 T. EGS4 PENELOPE(Mo) PENELOPE(SBR) Beam DPF DPF DPF(Mo:EGS4) DPF DPF(SBR:EGS4) DPF(SBR:Mo) Co ± ± MV ± ± MV ± ± MV ± ± MV ± Effect of the depth and thickness of magnetic field The effect of a 5 T magnetic field (2 cm thick) applied to a 5 MV beam at various depths in a water phantom is shown in figure 3.7. Positioning the slice of magnetic field below the surface (0 to 2 cm depth) produced a maximum DPF of about Moving the position of the field from the surface to a depth of 0.5 to 2.5 cm yielded a DPF of.9 at the surface of the phantom, which dropped to.65 at 0.3 cm depth before rising to a

59 35 maximum DPF of.95 at 0.5 cm depth. No change in either the maximum or minimum DPF was observed with the field positioned at greater depths. DPF (B/B=0) Effect of B=5T slice at different depths 0-2cm cm 2-4cm 4-6cm 7-9cm Depth (cm) Figure 3.7: Dose distribution of a 5 MV beam with a slice of 5 T transverse magnetic field (2 cm thick) applied at different depths in the water phantom. Also investigated was the effect of different thicknesses of a uniform magnetic field on the depth-dose of a 5 MV beam (in water). Figures 3.8 (a), (b), (c), and (d) plot the DPFs obtained in the presence of a 2, 5, and 0 T magnetic field slice of thickness, 2, 3, and 4 cm (centred at 8 cm depth), respectively. The maximum and minimum DPFs were neither affected by an increase or reduction in the magnetic field thickness (from 2 cm), nor were the widths of the dose enhancement and dose reductions. The only effect from varying the field thickness was an alteration in the range over which unity DPF is maintained between maximum and minimum DPF. While reducing the field thickness from 2 cm to cm eliminated the region of unity DPF, increasing the thickness from 2 cm to 3 or 4 cm expanded the region of unity DPF. Similar trends were observed for 6, 0, and 24 MV photon beams subjected to a 5 T magnetic field of different thicknesses, as shown in figures 3.9 (a), (b), (c), and (d) respectively.

60 36 DPF (a) Effect of a cm thick magnetic field B=0 B B= Depth (cm) B=2T B=5T B=0T DPF (b) Effect of a 2cm thick magnetic field B=0 B B= Depth (cm) B=2T B=5T B=0T Figure 3.8: Effect of the magnetic field thickness. Figures (a) and (b) show the effect on the depth-dose of a 5 MV beam when a 2, 5 and 0 T transverse magnetic field is applied at 7.5 to 8.5 cm and 7 to 9 cm depth (i.e. cm and 2 cm thick) in water, respectively.

61 37 DPF (c) Effect of a 3cm thick magnetic field B=0 B B= Depth (cm) B=2T B=5T B=0T DPF (d) Effect of a 4cm thick magnetic field B=0 B B= Depth (cm) B=2T B=5T B=0T Figure 3.8: Effect of the magnetic field thickness. Figures (c) and (d) show the effect on the depth-dose of a 5 MV beam when a 2, 5 and 0 T transverse magnetic field is applied at 6.5 to 9.5 cm and 6 to 0 cm depth (i.e. 3 cm and 4 cm thick) in water, respectively.

62 (a) 6MV beam: Effect of 5T magnetic field thickness cm cm cm cm DPF Depth (cm) DPF (b) 0MV beam: Effect of 5T magnetic field thickness Depth (cm) cm cm cm cm Figure 3.9: Effect of the magnetic field thickness. Figures (a) and (b) compare the effect of a 5 T transverse magnetic field of different thicknesses ( to 4 cm) on the depth-dose (in water) of a 6 and 0 MV beam respectively.

63 39 DPF (c) 5MV beam: Effect of 5T magnetic field thickness Depth (cm) cm cm cm cm DPF (d) 24MV beam: Effect of 5T magnetic field thickness Depth (cm) cm cm cm cm Figure 3.9: Effect of the magnetic field thickness. Figures (c) and (d) compare the effect of a 5 T transverse magnetic field of different thicknesses ( to 4 cm) on the depth-dose (in water) of a 5 and 24 MV beam respectively.

64 Discussion The effect of a transverse magnetic field on the dose distribution of high-energy photon beams was a dose enhancement (increase in DPF) at depths approaching and entering the magnetic field (i.e. between 5.5 and 7.5 cm). This dose perturbation was followed by a region of dose reduction (decrease in DPF) at depths exiting and beyond the magnetic field (i.e. between 8.5 and 0.5 cm), where the DPF returned to unity at about 2 cm depth. The region of dose enhancement arises from secondary electrons on average having an initial direction downstream (as shown in the following chapter). In the absence of a magnetic field, this leads to dose being deposited some distance downstream. The effect of the transverse magnetic field is to reduce the average distance between the depth at which an electron originates and the depth at which most of its energy gets deposited. This could be pictured as due to the electrons spiraling around the transverse magnetic field vector which reduces their depth of interaction and the depth of any secondary particles they produce. As shown in figure 3., the radius of curvature of an electron subjected to a magnetic field, and its mean free path (in water) between interactions, are both energy dependent. The figure also shows the cyclotron radius of an electron to be several orders of magnitude greater than its mean free path. This might lead to the erroneous conclusion that it is not possible for the magnetic field to influence the dose distribution. It must be remembered however that most electron interactions produce negligible change in the electron trajectory. Therefore, more significant than the mean free path is the mean distance an electron must travel before its trajectory is altered from its original path by one radian. As long as this distance is not significantly smaller than the radius of curvature we expect to see an effect. Alternatively, one could follow the approach of Bielajew, who compared the radius of an electron in a magnetic field to its range, and derived a rule of thumb showing these lengths become comparable in water at a magnetic field strength of approximately two thirds of a Tesla for relativistic energies [53]. Note that this result

65 4 is independent of electron kinetic energy as both the range and the radius are linearly dependent on kinetic energy for relativistic electrons. This rule of thumb does not apply at lower energies where the radius becomes proportional to the square root of the kinetic energy (refer to figure 3.). This is reflected in figure 3.0 which shows the mean distance travelled along the beam direction by electrons (of different energies) as a function of magnetic field. It can be seen that electrons with an energy less than MeV are not significantly affected. According to the secondary electron spectrum of a 5 MV beam as shown in figure 3., around 40% of secondary electrons have energies of MeV or higher. Thus, it is primarily these electrons which are responsible for the effects observed. It is also apparent from this figure that magnetic field strengths beyond 5 T will not produce significantly different dose enhancements, since it is at 5 T that the minimum distance an electron travels in the beam direction from its origin is observed. (A comprehensive study of the effect of magnetic field strength on the range of different energy electrons appears in the subsequent chapter.) Range along beam axis (cm) Influence of magnetic field on mean depth of electrons Magnetic field (T) 0.2MeV 0.5MeV MeV 2MeV 5MeV 0MeV Figure 3.0: Influence of a magnetic field on the mean distance an electron travels along the beam direction from its origin at 6.9 cm depth.

66 42 Consequently, higher energy electrons suffer a greater deviation in their path due to the magnetic field than lower energy electrons, resulting in shallower depths of interaction and production of any secondary particles. This increase in dose at shallower depths gives rise to the dose enhancement observed in the region approaching the magnetic field, where the distribution of particle energies, depths of interaction, and ranges give rise to its breadth. Number of electrons e Electron spectra for 5MV beam cm cm cm cm cm 0 5e+06 e+07.5e+07 Energy (ev) Figure 3.: Secondary electron spectrum of a 5 MV photon beam at different depths (5.5 to 0.5 cm) in water. The largest maximum DPF (.9) occurred with a field strength of 5 T, where stronger magnetic fields failed to yield larger maximum DPFs due to fewer low-energy electrons being able to escape the magnetic field as their radii of curvature became too confined. This also explains the steep fall-off in the DPF between the maximum and minimum value inside the magnetic field. The region of dose reduction corresponds to the absence of electrons, and any secondary particles they produce, that would otherwise be present in the absence of magnetic field. Thus, the primary dose contributors in this

67 43 region are photons (since they are unaffected by the magnetic field) and any secondary particles they produce. The reduction in minimum DPF yield with increasing magnetic field strength is due to fewer electrons escaping the magnetic field since their smaller radii of curvature reduces their depth of interaction. The PENELOPE elastic scattering parameters C and C 2 had no influence on the results, owing to the code s improved modelling of soft energy losses [38]. Decreasing the PENELOPE electron and photon low-energy transport cutoffs from 0 kev to kev also had no effect on the DPF or the low-energy electron spectrum. Doubling the number of scoring bins (by halving their depth) had an effect on the maximum and minimum DPFs. The small enhancement in the maximum DPF with smaller bins is attributed to the improved resolution of the position of maximum DPF. For example, an enhancement in the maximum DPF of % was observed for the 5 MV and 0 T combination, which shifted from a depth of 6.9 cm to 7. cm. Enhancements of up to 6% were observed for all other magnetic field combinations with 5 MV, some resulting in minor shifts in the maximum DPF to greater depths (e.g. 20 and 00 T maximum DPF shifted from 6.9 to 7.0 cm depth). Conversely, the minimum DPF exhibited a reduction, especially at higher magnetic fields. For example, a reduction in the minimum DPF of 33% was observed for the 5 MV and 00 T combination. Despite an additional bin at the 9 cm boundary (i.e. bins at 8.9, 9.0, and 9. cm instead of 8.9 and 9. cm), the position of the minimum DPF remained fixed at 9. cm depth. The reduction in the minimum DPF arises from the presence of the extra bin at 9 cm depth. It scores any dose depositions immediately beyond the magnetic field that would have otherwise been deposited in the 9. cm bin (for the case of 0.2 cm bins). This gives rise to the steeper fall-off in the dose reduction at the 9 cm field boundary. The lower minimum DPFs exhibited by higher magnetic fields is due to the electrons smaller cyclotron radii (and hence, shallower depths of interaction), which results in fewer electrons escaping the magnetic field.

68 44 Higher energy photon beams subjected to a 5 T magnetic field exhibit larger maximum and smaller minimum DPFs, owing to their longer ranges and correspondingly greater yields of secondary electrons at these depths. Of the electrons generated within the vicinity of the magnetic field, those with a range sufficiently larger than their cyclotron radius have a higher probability of escaping the magnetic field. This leads to a broadening in the dose enhancement and dose reduction at the magnetic field boundaries, which is wider for higher energy photon beams due to the larger range of secondary electrons set into motion. The 85% increase in the maximum DPF of a 5 MV photon beam subjected to the slice of 5 T transverse magnetic field at the phantom s surface is due to the large population of low-energy electrons in the build-up region (i.e. distance from the surface to the depth at which maximum dose occurs), which is about 3 cm for a 4 4 cm 2 field. As the ranges of these electrons (in water) are only fractions of a centimeter (e.g. a 00 kev electron has a 0.0 cm range in water), the presence of a magnetic field reduces their depth of interaction, thereby leading to an increase in DPF. This also explains the consistent maximum and minimum DPFs obtained with the slice of magnetic field applied beyond the build-up region. The DPF realised in this study will be greater than those attainable with a more realistic magnetic field distribution as demonstrated in the work by Jette [67]. Altering the thickness of the magnetic field (i.e. depth over which it is applied) had no affect on the maximum and minimum DPFs. According to the 5 MV secondary electron spectrum in figure 3., the majority of electrons at these depths have energies less than MeV, which corresponds to a range (in water) of less than 0.4 cm. When subjected to a 5 T magnetic field, these electrons have a cyclotron radius of less than 0. cm, and therefore remain trapped within the field unless they are near to one of its boundaries.

69 Conclusion The application of a slice of uniform transverse magnetic field to high-energy photon beams results in localised regions of dose enhancement and dose reduction. The region of dose enhancement occurs at depths approaching and entering the slice of magnetic field, while the region of dose reduction is present at depths exiting and beyond the slice. The dose enhancement arises from a reduction in the depth of interaction of electrons and any secondary particles they produce, as they travel through the transverse magnetic field. The largest enhancement (maximum DPF of.9) was observed with 5 T, where further increments in magnetic field (up to 00 T) failed to produce higher maximum DPFs. The breadth of this dose enhancement region is attributed to the spread of energy, depth of interaction, and range of the electrons. Correspondingly, there is a region of dose reduction immediately beyond the magnetic field slice caused by a deficiency of electrons in this region (since photons are unaffected by the magnetic field). The decreasing minimum DPF with increasing magnetic field is due to the smaller cyclotron radii of electrons, which reduces their depth of interaction and probability of escaping the magnetic field. The PENELOPE maximum and minimum DPFs were 9% enhancement and 77% reduction respectively, which are slightly smaller than Li s respective EGS4 results of 97% and 79%. The PENELOPE DPFs were mostly within 4% of those obtained with EGS4, where the minor discrepancies between the codes were not resolved. Reducing the PENELOPE photon and electron low-energy transport cutoff to kev and altering the elastic scattering parameters C and C 2 had no effect on the results. Increasing the bin resolution (by halving the depth of the scoring bins from 0.2 to 0. cm) produced a small increase in the maximum DPFs and a corresponding reduction in the minimum DPFs. It did not, however, resolve the discrepancies between the PENELOPE and EGS4 results. The application of a 5 T magnetic field to different energy photon beams revealed larger maximum and smaller minimum DPFs with higher beam energies. This is because

70 46 higher energy photons interact at greater depths, resulting in the presence of more electrons within the vicinity of magnetic field. The electron deficiency beyond the magnetic field gives rise to the reduction in the minimum DPF, which was more severe for higher energy beams. Applying a slice of 5 T magnetic field at the surface of the water phantom produced a substantial 85% increase in the maximum DPF for the 5 MV beam. Altering the thickness of the magnetic field had no effect on the maximum and minimum DPFs, although it did produce wider regions of unity DPF inside the slice of magnetic field. This could be therapeutically beneficial for the treatment of tumours close to radiationsensitive structures in the body, where the magnetic field thickness (chosen according to the distance between the tumour and critical structure) would be aligned in such a way to maximise dose to the tumour whilst sparing critical tissue.

71 CHAPTER 4 EFFECT OF A TRANSVERSE MAGNETIC FIELD ON THE ELECTRON DISTRIBUTION OF HIGH-ENERGY PHOTON BEAMS 4. Introduction In chapter 3, the application of a transverse magnetic field to high-energy photon beams was shown to alter the dose deposition in such a way as to produce localised regions of dose enhancement and dose reduction. The current chapter investigates the influence of a transverse magnetic field on the spatial distribution of secondary electrons produced from these photon beams. It also explores the potential of a magnetic field to alter the corresponding relative biological effectiveness of this radiation through a change in the low-energy secondary electron spectrum. Results appearing in sections 4.3. and of this chapter have been published in a peer-reviewed journal article [48]. When radiation traverses matter, it can deposit its energy via the processes of ionisation or excitation of absorber atoms. In tissue, these energy depositions can induce lesions in the DNA of cells, which if incompletely or incorrectly repaired may result in lethal or mutagenic radiobiological effects [33 35]. It is commonly accepted that the initiation of these effects depends on the spatial distribution of lesions [68]. Isolated DNA damage such as single-strand breaks (SSBs) are generally repaired efficiently [35], while closely spaced lesions such as double-strand breaks (DSBs), where two or more SSBs occur on opposing strands within 0 to 20 base pairs [69], may lead to irreparable DNA damage. It has also been postulated that substantial biological damage results from clusters of DNA lesions (formed when low-energy electrons produced from electron inelastic collisions interact in close proximity to one another) as they are more prone to misrepair [70 72]. 47

72 48 Figure 4.: Relationship between relative biological effectiveness (RBE) and mean linear energy transfer (LET) for cell killing, where the three curves correspond to different levels of cell survival, or surviving fraction (SF) [74, 75]. For the same absorbed dose, or average energy deposited per unit mass, it is well known that different radiation types can induce different biological effects. This is quantified by the term relative biological effectiveness (RBE), or the ratio of the absorbed dose of a reference radiation to the absorbed dose of a test radiation to produce the same biological effect. Thus, for an equivalent radiation exposure, a higher RBE results in greater biological damage. Generally, RBE increases with increasing linear energy transfer (LET), which is the rate of energy loss per unit distance along the path of a charged particle [73]. This is shown in figure 4. with a plot of RBE as a function of LET for three different levels of cell survival, or surviving fraction (SF) [74, 75], where a maximum RBE occurs at an LET between 00 and 200 kev/µm. As an electron loses energy its LET increases, and generally, so does its RBE. Therefore short-range low-energy electrons have a higher probability of inducing lethal damage to the DNA of cells (via strand breaks) than more energetic electrons. A 20 kev electron, for example, has a 9 µm range in tissue which is roughly the diameter of a typical human cell.

73 49 When an electron is subjected to a magnetic field, the Lorentz force confines its trajectory, and hence its energy deposition, to a smaller volume. Since the radius of curvature of an electron is known to decrease with decreasing energy, it is possible that the application of a magnetic field will not only affect the macroscopic absorbed dose distribution, but that it will also affect the distribution of ionisation clusters on a nanometre scale - in DNA. While the effect of a magnetic field on the absorbed dose distribution has been examined, and the potential for magnetic fields to alter the RBE has been mentioned [5, 53, 6, 76], absent from the literature is the study of a magnetic field s influence on the electron distribution from high-energy photon beams and any related change to their RBE. Considering the implementation of magnetic fields into radiotherapy has become practically feasible with the recent development of an integrated.5 T MRI scanner and 6 MV linear accelerator (for soft-tissue tumour imaging, position verification, and treatment monitoring in image-guided radiotherapy [60, 62, 77]), these effects should be studied to ascertain their importance in treatment planning. This chapter endeavours to explore these effects by using Monte Carlo PENELOPE simulation to investigate the influence of a transverse magnetic field on the secondary electron spectrum of various photon beams. In the course of obtaining secondary electron spectra with and without a magnetic field, several peaks consistently featured at energies below 700 ev. Since their origin is most likely related to atomic relaxation events, a number of simulations were performed to determine the energies of characteristic radiation in water (i.e. hydrogen and oxygen atoms). According to the plot of absorption and scattering contributions towards the total attenuation (in water) in figure 4.2 (a), the predominant mode of interaction of photons with relatively low energies is the photoelectric process. In this process, the incident photon undergoes an interaction with an absorber atom in which the photon transfers its energy, hv, to one of the orbital electrons of the bound shells of the atom. This photoelectron, whose most probable origin is the K shell of the atom, is ejected from the atom

74 50 with an energy, E e, given by E e = hv E b (4.) where E b is the binding energy of the photoelectron in its original shell. The vacancy created by the ejected photoelectron is filled through the capture of a free electron from the medium and/or rearrangement of electrons from other shells that have a lower binding energy. This process generates characteristic X-ray photons and/or Auger electrons. The energy of the characteristic radiation is the surplus energy liberated when an electron drops from its outer shell to a shell closer to the nucleus (i.e. difference in their binding energies). The binding energies for hydrogen and oxygen are shown in table 4.. The PENELOPE atomic photoelectric cross sections of hydrogen (K shell) and oxygen (K, L, L 2, and L 3 shells) are shown in figure 4.2 (b). Table 4.: Binding energies of hydrogen and oxygen [78]. Element Shell Electronic level Binding energy (ev) H K s 3.6 O K s 543. L 2s Simulation methods As photon trajectories are unaltered by the presence of a magnetic field, the location of any first generation secondary electrons (i.e. descendants from primary photons) is also unaffected. Simulations were performed to obtain the first generation secondary electron spectra in water (in the absence of a magnetic field) for Co 60, 6, 0, and 5 MV and, 5, 0, and 5 MeV photon beams. These simulations used electron and photon energy cutoffs of 0 kev and a total of 0 8 primary histories. Simulations were also performed to obtain the secondary electron spectrum (all generations) for a 5 MV beam with and without a slice of transverse magnetic field

75 5 µ (cm 2 /g) e+07 e (a) Photoelectric absorption and scattering contributions in water Total attenuation Photoelectric absorption Incoherent (Compton) scattering Coherent (Rayleigh) scattering Photon energy (ev) Photoelectric cross section (barn) e+07 e PENELOPE photoelectric cross sections for hydrogen and oxygen (b) Photon energy (ev) H Total (Kshell) O Total O Kshell O Lshell O L2shell O L3shell Figure 4.2: Figure (a) plots the absorption and scattering contributions towards the total attenuation of water using data obtained from NIST [36]). Figure (b) plots the PENE- LOPE atomic photoelectric cross sections for hydrogen (K shell) and oxygen (K, L, L 2, and L 3 shells) [38]. (between 7 and 9 cm depth). Magnetic fields of 2, 5, 0, and 20 T were chosen for this study. The total number of primary photon histories was 0 8 to ensure a statistical uncertainty within 98% confidence level. These simulations used the same water phantom and field size as those used to obtain the depth-dose curves in chapter 3. That is, a water

76 52 phantom cm 3 (width height depth) and a field size 4 4 cm 2 at 00 cm source to surface distance (SSD). Transport cutoffs were 0 kev for electron and photon transport and kev for the parameters for W cc, W cr, and the elastic scattering parameters C and C 2 were set to The electrons were binned along central axis according to their energy (up to MeV) and depth using bin intervals of 0 kev and 0.2 cm respectively. Electron spectra were plotted for five different regions of interest within the vicinity of the magnetic field: 5.5 to 6.5 cm depth (before the magnetic field slice), 6.5 to 7.5 cm (entering the magnetic field), 7.5 to 8.5 cm (inside the magnetic field), 8.5 to 9.5 cm (exiting the magnetic field), and 9.5 to 0.5 cm (beyond the magnetic field). The simulations were repeated with bin intervals of 00 ev to obtain an electron spectrum up to 0 kev. These simulations used transport cutoffs of 00 ev for electrons and photons, and the parameters W cc and W cr. The ratio of spectra obtained with and without magnetic field was constant over most of the energy range. Additional simulations were performed with, 3, and 4 T magnetic fields to produce a plot of the (constant) ratio of electron population with and without magnetic field as a function of field strength. In the course of obtaining the secondary electron spectra (up to 0 kev), several peaks were observed at energies below 700 ev. The unresolved peak between 450 and 550 ev prompted simulations with smaller energy bins of 0 ev (rather than 00 ev) in attempt to resolve it. As the PENELOPE interaction models and the associated databases for particle interaction are limited to an energy of 00 ev (i.e. particles with an energy below 00 ev are no longer transported), a variable named ecut (set to kev) was used to force all electrons with an energy below kev to be put onto the secondary stack prior to absorption. This stack is used to store the information of secondary particles (emitted from primary particle interactions), which are simulated in chronological succession after completion of each primary track. These simulations were performed with 0 7 (rather than 0 8 ) primary histories, owing to longer simulation times with lower energy cutoffs. Additional simulations were performed in order to establish whether the spectral

77 53 peaks are the result of atomic relaxation events in water (as they occur at typical energies for characteristic radiation in oxygen). These simulations used the PENELOPE ILB(4) label to track particles emitted from atomic relaxation and identify the shell from which they were released. The transport parameters used in these simulations were identical to those used to obtain the electron spectrum up to kev. Electrons retrieved from the stack with a non-zero ILB(4) label (i.e. emitted from atomic relaxation) were binned in cylindrical scoring volumes of 0.5 cm radius 0.2 cm depth according to their energy and position along central axis. In PENELOPE, the direction of a particle is defined by u, v and w which corresponds to the projection of its direction on the x, y, and z axes, respectively. Since the effect of a transverse magnetic field on electron trajectories is greatest for those moving perpendicular to the field and least for those travelling parallel to it, a number of simulations were performed to study the angles by which electron paths deviate from their initial direction (u, v, w = 0, 0, ) as they travel through water. These simulations focused on the change in an electron s w-value, where a value of zero corresponds to an electron deviated 90 degrees from the beam axis, while a value of unity describes an electron moving parallel to the beam. The mean w-values of first generation electrons were investigated with Co 60, 6, 0, and 5 MV and 0., 0.5,, 5, 0, and 5 MeV photon beams (in the absence of a magnetic field). The simulations were performed with 0 6 primary histories and C and C 2 values of 0.05, and made use of the PENELOPE ILB() and ILB(2) labels to identify first generation electrons and the type of parent particle respectively. When a secondary electron with an ILB() > and an ILB(2) = 2 (i.e. descendant of a photon) was taken off the secondary stack, its w-value was binned (according to energy) and its transport terminated. Also investigated was the mean distance that an electron travels (in the absence of a magnetic field) before the w-value of its initial trajectory (u, v, w = 0, 0, ) is deviated by a given angle up to 90 degrees (i.e. w = 0). This study used monoenergetic electron beams of 0., 0.5,, 5, 0, and 5 MeV, and a total of 0 bins to score w-values between.0 and

78 54 zero. The simulations were performed with a total of 0 6 primary histories and energy cutoffs of 0. MeV for electron beams with an energy of MeV and higher, and cutoffs of 0.0 MeV for lower energy electrons. The electrons were transported until their energy reached half of its initial value, where its w-value was binned prior to its termination. Additional simulations were performed for each of the electron beams to determine the mean range of electrons in water as a function of energy. These simulations used transport cutoffs of 0.0 MeV for all beam energies. A detailed investigation of the effect of a transverse magnetic field on the range and spatial distribution of electrons was also performed to better understand the changes observed in the depth-dose curves of chapter 3. In this study, monoenergetic electron beams of 0.0, 0.05, 0., 0.5,, 5, 0, and 5 MeV (i.e. typical electrons produced from the interaction of a 5 MV photon beam) were subjected to a slice of,.5, 2, 3, 5, 0, 20, 30, 40, 50, 75, and 00 T magnetic field between 7 and 9 cm depth (in water). Five simulations were performed for each electron beam, where the primary electrons were started from a depth of: 6.9 cm (immediately before the magnetic field); 7.5, 8.5, and 8.9 cm (inside the magnetic field); and 9. cm (immediately beyond the magnetic field). The initial direction of primary electrons was along the z-axis (w = ), and perpendicular to the transverse magnetic field, which was in the direction of the positive x-axis. The simulations used low-energy electron and photon cutoffs of 00 ev and a total of 0 5 primary electron histories. For each simulation, the electron s y and z-range was calculated as the distance between its origin and endpoint (prior to absorption), and a mean of these ranges was determined at the completion of the simulation. Since a magnetic field along the positive x-axis exerts a Lorentz force on electrons in the direction of the negative y-axis, its influence on the electron spatial distribution was investigated by tallying electron populations on either side of the plane y = 0 (according to the y-coordinate of their final position). The ratio of electrons with a negative y-endpoint (y < 0) to those with a positive y-endpoint (y > 0) was calculated for the five different starting depths. The effect of a magnetic

79 55 field on the electron distribution along the z-axis (beam axis) was also investigated by calculating a ratio of the number of electrons with a final position downstream of their start position (z > z start ) to those with an end position upstream of the start (z < z start ). 4.3 Simulation results and discussion Figures 4.3 (a) and (b) plot the first generation electron spectra (in water) for polyenergetic photon beams of Co 60, 6, 0, and 5 MV and monoenergetic photon beams of, 5, 0, and 5 MeV, respectively. Most of these electrons are produced in Compton scattering events, as this is the dominant photon interaction mechanism (in water) between about 30 kev and several MeV. The large population of low-energy electrons stems from the higher Klein-Nishina cross section that photons undergo small angle Compton scattering (refer to figure 2.2). The electron spectra of monoenergetic photon beams exhibit a peak just below the photon energy, which corresponds to the maximum energy transferred to a Compton electron (i.e. when the photon is backscattered 80 from the initial direction of its motion). This peak does not appear in the electron spectra of polyenergetic photon beams as there are fewer high-energy electrons owing to the small probability of high-energy photons. Figures 4.4 (a) and (b) show the spectra of secondary electrons of all generations for a 5 MV beam obtained with and without a 5 T transverse magnetic field (between 7 and 9 cm depth) respectively. These spectra show the electron population in five cmdeep regions within the vicinity of the magnetic field: 5.5 to 6.5 cm depth (before the magnetic field slice), 6.5 to 7.5 cm (entering the magnetic field), 7.5 to 8.5 cm (inside the magnetic field), 8.5 to 9.5 cm (exiting the magnetic field), and 9.5 to 0.5 cm (beyond the magnetic field). The spectra obtained with magnetic field exhibit differences in the electron population below about MeV which are not present in the corresponding spectra obtained without magnetic field.

80 56 Number of electrons e+09 e+08 e+07 e First generation electrons for polyenergetic photon beams (a) 0 5e+06 e+07.5e+07 Energy (ev) Co 60 6MV 0MV 5MV Number of electrons e+09 e+08 e+07 e First generation electrons for monoenergetic photon beams (b) 0 5e+06 e+07.5e+07 Energy (ev) MeV 5MeV 0MeV 5MeV Figure 4.3: First generation electron spectra for polyenergetic and monoenergetic photon beams (in water). Figure (a) plots the first generation electron spectra for Co 60, 6, 0, and 5 MV beams. Corresponding electron spectra for, 5, 0, and 5 MeV monoenergetic photon beams are shown in figure (b).

81 57 Electron spectra for 5MV beam with B=zero Number of electrons e (a) cm cm cm cm cm e+06 e+07 Energy (ev) Electron spectra for 5MV beam with B=5T Number of electrons e (b) cm cm cm cm cm e+06 e+07 Energy (ev) Figure 4.4: Secondary electron spectra (all generations) for a 5 MV beam with depth (in water). Figures (a) and (b) plot the electron spectra in the presence and absence of a slice of 5 T transverse magnetic field (7 to 9 cm depth), respectively.

82 Influence of a magnetic field on electron spectra below MeV Figures 4.5 (a), (b), (c), and (d) plot a ratio of the electron population (below MeV) in the presence and absence of a 2, 5, 0, and 20 T transverse magnetic field (7 to 9 cm depth), respectively. For all magnetic fields investigated, a maximum electron population (below MeV) occurred in the region entering the magnetic field (6.5 to 7.5 cm depth) and a minimum population in the region exiting the field (8.5 to 9.5 cm depth). The presence of a 5 T magnetic field produced the largest augmentation in electron population between 6.5 and 7.5 cm, which was 54% higher than that obtained in the absence of field. It also yielded the smallest electron population between 8.5 and 9.5 cm, which was 48% lower than that obtained without magnetic field. Reducing the magnetic field from 5 to 2 T resulted in reductions of 30% and 22% in the maximum and minimum electron populations respectively. However, increasing the magnetic field beyond 5 T failed to produce larger maximum and minimum electron populations in these regions, although variations were observed in the populations of other regions. In the region before the magnetic field (5.5 to 6.5 cm) the electron population increased with stronger magnetic fields, while in the region beyond the field (9.5 to 0.5 cm) it decreased. Inside the magnetic field (7.5 to 8.5 cm), the ratio of electron population was unity for all magnetic fields except 2 T, which exhibited a 4% increase. The regions of maximum and minimum electron population correspond with the regions of maximum dose enhancement and dose reduction in the depth-dose profiles of chapter 3 (refer to figure 3.4). This suggests that the effect of a magnetic field on the dose deposition is associated with a change in the secondary electron spectrum. For an electron moving in a transverse magnetic field, its depth of interaction is reduced when its range is comparable to or greater than its cyclotron radius. This in effect causes an upstream migration of electrons (with sufficient range), and hence, any secondary electrons they produce from interactions within the medium (water). Of the

83 59 Electron spectra for 5MV beam with B=2T (7-9cm) Number of electrons (B/B=0) (a) cm cm cm cm cm e+06 Energy (ev) Electron spectra for 5MV beam with B=5T (7-9cm) Number of electrons (B/B=0) (b) cm cm cm cm cm e+06 Energy (ev) Figure 4.5: Normalised electron spectra (below MeV) for a 5 MV beam. Figures (a) and (b) plot a ratio of the electron population in the presence and absence of a 2 and 5 T transverse magnetic field (7 to 9 cm depth), respectively.

84 60 Electron spectra for 5MV beam with B=0T (7-9cm) Number of electrons (B/B=0) (c) cm cm cm cm cm e+06 Energy (ev) Electron spectra for 5MV beam with B=20T (7-9cm) Number of electrons (B/B=0) (d) cm cm cm cm cm e+06 Energy (ev) Figure 4.5: Normalised electron spectra (below MeV) for a 5 MV beam. Figures (c) and (d) plot a ratio of the electron population in the presence and absence of a 0 and 20 T transverse magnetic field (7 to 9 cm depth), respectively.

85 6 descendant electrons, those with an energy of 0.5 MeV or lower will deposit their energy locally since their ranges are less than the 0.2 cm depth of the scoring bins. It is therefore the upstream migration of electrons that gives rise to the population increase in the regions before and entering the magnetic field (5.5 to 6.5 cm and 6.5 to 7.5 cm), and the subsequent depletion of electrons (minimum population) further downstream in the regions exiting and beyond the magnetic field (8.5 to 9.5 cm and 9.5 to 0.5 cm). The smaller variations in electron population observed with 2 T as opposed to 5, 0, and 20 T are attributed to the electrons larger cyclotron radii in weaker magnetic fields, and hence, lower probability of depositing their energy further upstream. Inside the magnetic field (7.5 to 8.5 cm), there was little change in the electron population with and without a magnetic field of 5 T or stronger. (A similar observation was made in the depth-dose profiles in chapter 3). This is because the electron population in this region is maintained by an upstream migration of electrons (i.e. shallower depths of interaction) which would have otherwise, in the absence of a magnetic field, deposited dose further downstream. The increase in electron population exhibited by the 2 T field is attributed to the electrons larger radii of curvature, and hence, deeper depths of interaction (i.e. fewer electrons can escape the magnetic field to deposit their energy upstream). In the region beyond the magnetic field (9.5 to 0.5 cm), a depletion of electrons (resulting from the upstream migration) gives rise to the comparatively smaller population. Here, the majority of electrons are of first generation (i.e. produced from photon interactions) as photon trajectories are not influenced by a magnetic field Influence of a magnetic field on electron spectra below 0 kev As an electron loses energy its LET increases and so does its relative biological effectiveness (RBE). It is therefore possible that the increase in low-energy electron population in the region entering the magnetic field (6.5 to 7.5 cm) may correspond to an increase in RBE, and conversely, the reduction in population in the region exiting the magnetic field (8.5 to 9.5 cm) may correspond to a reduction in RBE.

86 62 The larger differences in the electron population with decreasing energy led to a study of the electron spectra below 0 kev (smallest bin in the electron spectra below MeV). Figures 4.6 (a) and (b) show the resulting spectra obtained with and without a 5 T magnetic field, respectively, using bin intervals and energy cutoffs of 00 ev. These spectra reveal an unresolved peak between 450 and 550 ev (i.e. centres of 00 ev bins) superimposed on a Compton continuum. In the absence of a magnetic field, the electron distribution appears to be approximately the same in all five regions. However, when subjected to a 5 T magnetic field the spectra disperse in a similar fashion to that exhibited by the electron spectra in figure 4.4, where the largest and smallest populations are observed in the regions 6.5 to 7.5 cm and 8.5 to 9.5 cm respectively. A ratio of the electron population obtained with and without a 5 T magnetic field, as shown in figure 4.7, reveals a constant ratio between about 600 and 0000 ev. This is also apparent in the ratio of electron spectra obtained with and without a, 2, 3, 4, 0, and 20 T transverse magnetic field. A plot of the mean ratio as a function of magnetic field (in the five different regions) is shown in figure 4.8. In the region before the slice of magnetic field (5.5 to 6.5 cm depth), the ratio of electron population rises above unity and continues to increase with magnetic fields greater than 2 T. In the region entering the magnetic field (6.5 to 7.5 cm depth), the electron population augments with increasing field strength, reaching a maximum increase of 52% at 5 T before decreasing by up to 0% at stronger fields. Inside the slice of magnetic field (7.5 to 8.5 cm depth), the ratio of electron population is approximately unity for magnetic fields beyond about 4 T, while at weaker field strengths it rises above unity by as much as 8%. In the region exiting the magnetic field (8.5 to 9.5 cm depth), the ratio rapidly decreases with increasing field up to about 4 T where the ratio is 36% below unity. There is little change in the ratio between field strengths of 4 to 20 T. Sub-unity ratios are observed in the region beyond the magnetic field (9.5 to 0.5 cm depth), where the ratio can be seen to decrease with increasing magnetic field by as much as 32% at 20 T. While the presence of magnetic field has no affect on the trajectories of photons, it

87 63 Number of electrons e+07 e MV beam: low-energy electrons (< 0keV) with B=zero (a) cm cm cm cm cm Energy (ev) Number of electrons e+07 e (b) 5MV beam: low-energy electrons (< 0keV) with B=5T cm cm cm cm cm Energy (ev) Figure 4.6: Secondary electron spectra (below 0 kev) for a 5 MV beam. Figures (a) and (b) plot the electron spectra in five depth regions in the presence and absence of a 5 T transverse magnetic field (7 to 9 cm depth), respectively.

88 64 Number of electrons (B/B=0) MV beam: electron spectra (< 0keV) with B=5T cm cm cm cm cm Energy (ev) Figure 4.7: Normalised electron spectra (below 0 kev) for a 5 MV beam. A ratio of the electron population in five depth regions in the presence and absence of a 5 T transverse magnetic field (7 to 9 cm depth). Number of electrons (B/B=0) Effect of magnetic field on electron spectra (< 0keV) cm cm cm cm cm Magnetic field (T) Figure 4.8: Ratio of electron spectra (below 0 kev) for a 5 MV beam as a function of magnetic field. A ratio of the electron population in five depth regions in the presence and absence of a, 2, 3, 4, 5, 0, and 20 T transverse magnetic field (7 to 9 cm depth).

89 65 can influence their spatial distribution. This occurs when the photon is a descendant of an electron whose range is comparable to or greater than its cyclotron radius, leading to an alteration in its depth of interaction, and hence that of the secondary photon. Simulations were therefore performed to obtain the secondary photon spectra (below 0 kev) for a 5 MV beam in the presence and absence of magnetic field. Figures 4.9 (a) and (b) show the resulting photon spectra with and without a 5 T transverse magnetic field, respectively. Common to both spectra is a peak at 550 ev (centre of 00 ev bin) which has a higher intensity in the regions before and entering the magnetic field (5.5 to 6.5 cm and 6.5 to 7.5 cm) and a lower intensity in the regions exiting and beyond the field (8.5 to 9.5 cm and 9.5 to 0.5 cm). On either side of the peak, the comparatively smaller populations and insufficient statistics render it difficult to ascertain any influence of the magnetic field Influence of a magnetic field on electron spectra below kev The unresolved peaks between 450 and 550 ev in the electron spectra of figure 4.6 led to additional simulations of electron spectra (below kev) using a finer bin resolution of 0 ev as opposed to 00 ev. Figures 4.0 (a) and (b) show the electron spectra (below kev) for a 5 MV beam in the presence and absence of a slice of 5 T transverse magnetic field (7 to 9 cm depth), respectively. The corresponding ratio of electron population with and without magnetic field is shown in figures 4. (a), (b), (c), and (d) for 2, 5, 0, and 20 T magnetic fields, respectively. The 550 ev peak in the photon spectra (below 0 kev) and appearance of several peaks between 475 and 685 ev in the electron spectra (below kev) prompted further simulations to establish their identity and origin. As the K shell binding energy of oxygen (543. ev) is within this range, the simulations targeted electrons and photons produced from atomic relaxation events in water (i.e. hydrogen and oxygen atoms). Figures 4.2 (a) and (b) show the resulting spectra of atomic relaxation electrons in the presence and absence of a 5 T magnetic field, respectively. A plot of atomic relaxation photons is shown in figure 4.2 (c).

90 66 5MV beam: secondary photons (< 0keV) with B=zero Number of photons (a) cm cm cm cm cm Energy (ev) 5MV beam: secondary photons (< 0keV) with B=5T Number of photons (b) cm cm cm cm cm Energy (ev) Figure 4.9: Photon spectra (below 0 kev) for a 5 MV beam. Figures (a) and (b) plot the photon spectra with and without a 5 T transverse magnetic field (7 to 9 cm depth), respectively.

91 67 e+07 (a) 5MV beam: low-energy electrons (<kev) with B=zero Number of electrons e Energy (ev) cm cm cm cm cm Number of electrons e+07 e (b) 5MV beam: low-energy electrons (<kev) with B=5T Energy (ev) cm cm cm cm cm Figure 4.0: Electron spectra (below kev) for a 5 MV beam. Figures (a) and (b) plot the electron spectra with and without a 5 T transverse magnetic field (7 to 9 cm depth), respectively.

92 68 Number of electrons (B/B=0) 5MV beam: electron spectra (< kev) with B=2T.6 (a) cm cm cm cm cm Energy (ev) Number of electrons (B/B=0) 5MV beam: electron spectra (< kev) with B=5T.6 (b) cm cm cm cm cm Energy (ev) Figure 4.: Normalised electron spectra (below kev) for a 5 MV beam. Figures (a) and (b) plot a ratio of the electron population in the presence and absence of a 2 and 5 T transverse magnetic field (7 to 9 cm depth), respectively.

93 69 Number of electrons (B/B=0) 5MV beam: electron spectra (< kev) with B=0T.6 (c) cm cm cm cm cm Energy (ev) Number of electrons (B/B=0) 5MV beam: electron spectra (< kev) with B=20T.6 (d) cm cm cm cm cm Energy (ev) Figure 4.: Normalised electron spectra (below kev) for a 5 MV beam. Figures (c) and (d) plot a ratio of the electron population in the presence and absence of a 0 and 20 T transverse magnetic field (7 to 9 cm depth), respectively.

94 70 Number of electrons (B/B=0) e+07 e (a) 5MV beam: atomic relaxation electrons with B=zero Energy (ev) cm cm cm cm cm Number of electrons (B/B=0) e+07 e (b) 5MV beam: atomic relaxation electrons with B=5T Energy (ev) cm cm cm cm cm Number of photons (B/B=0) e+07 e (c) 5MV beam: atomic relaxation photons with B=zero Energy (ev) cm cm cm cm cm Figure 4.2: Spectra of atomic relaxation electrons and photons (in water) for a 5 MV beam. Figures (a) and (b) plot the spectra of atomic relaxation electrons with and without a 5 T transverse magnetic field (7 to 9 cm depth), respectively. Atomic relaxation photons are plotted in figure (c).

95 7 Common to both the electron and atomic relaxation electron spectra are peaks at 475 ev and between 495 and 505 ev, whose origin is thus from atomic relaxation in oxygen. The PENELOPE binding energies for the K, L, L 2, and L 3 shells of oxygen are 543, 24, 4, and 4 ev, respectively [38], where the transition probabilities and energies of Auger electron production (in water) are given in table 4.2. Table 4.2: Energies and probabilities of Auger electron production in water [38]. Auger e- Energy (ev) Probability KLL 4.788E E-0 KLL E+02.62E-0 KLL E E-0 KL2L E+02.08E-02 KL2L E E-0 KL3L E E-0 The spectral peaks at 475, 495, and 505 ev in the secondary electron spectra therefore result from Auger electron emission. The peak at 475 ev is produced from KLL Auger electrons, while the broad peak around 500 ev arises from the emission of Auger electrons following atomic relaxations to the K shell from the L 3 and L 2 shells. The prominent peak at 685 ev, however, is not the result of Auger electron emission but an artefact of the Sternheimer-Liljequist model used to simulate soft inelastic collisions (refer to subsection of the 2006 PENELOPE manual [79]). The single peak at 525 ev, which features in both the low-energy photon and atomic relaxation photon spectra, corresponds with the K α characteristic X-ray emission from the excitation and relaxation of electrons within the atomic shells of oxygen. It occurs when an incident photon transfers sufficient energy to a K shell electron (in oxygen) to excite it into an outer, less-tightly bound shell, leaving a vacancy in the K shell. When this vacancy is filled by an electron dropping from either the L 2 or L 3 shell, a 529 ev photon is emitted (i.e. the difference between their binding energies).

96 Effect of magnetic field on the w-values of electrons The effect of a transverse magnetic field on electron trajectories is greatest for those moving perpendicular to the magnetic field and least for those travelling parallel to it. This observation prompted a series of simulations to gather information about the angles through which electron paths deviate from their initial direction (in water) in the absence of a magnetic field. These simulations focused on the distribution of w-values since it is this component of the electron s path which is parallel with the incident beam (z-axis) and perpendicular to the magnetic field (x-axis). A w-value of zero describes an electron travelling perpendicular to the field, while a w-value of unity describes an electron moving parallel to it. Figures 4.3 (a) and (b) plot the mean w-values of first generation electrons as a function of energy for Co 60, 6, 0, and 5 MV and 0.05, 0.0, 0.50,, 2, 5, 0, and 5 MeV photon beams, respectively. As shown in figure 2.2, the higher the energy of the Compton scattered photon the smaller its angle of deviation from its initial direction (w = ), and the larger the angular deviation of the Compton electron (refer to figure 2.3). The mean w-values of first generation electrons for monoenergetic and polyenergetic photon beams are shown in figure 4.3. Generally, for a given energy photon beam, the higher the electron energy the less it is deviated from the beam direction (w = ), except first generation electrons of 0., 0.5, and MeV beams, which exhibit a rapid drop in w-value at about 0.028, 0.33, and 0.8 MeV respectively. The maximum w-value corresponds to the maximum kinetic energy that can be transferred to a free electron from a Compton scattered photon. This occurs when the photon is scattered 80 degrees, where the electron moves in the forward direction in order to conserve momentum. Beyond the drop-off, the w-value increases with increasing energy, reaching a final value of about 0.5, 0.8, and 0.9 for 0., 0.5, and MeV photon beams respectively. The final w-value results from photoelectric interactions where the incident photon loses all of its energy in ejecting an orbital electron within the absorber atom. The kinetic energy given to this electron is the surplus from that required to free the electron (i.e. minus the binding energy).

97 (a) w-values of first generation electrons Mean w-value Co60 0 6MV 0MV 5MV Energy (MeV) 0.8 (b) w-values of first generation electrons Mean w-value MeV MeV MeV 0 5MeV 0MeV 5MeV Energy (MeV) Figure 4.3: Mean w-values of first generation electrons for the following photon beams: (a) Co 60, 6, 0, and 5 MV, and (b) 0., 0.5,, 5, 0, and 5 MeV.

98 74 Electrons moving parallel to a magnetic field are unaffected by its presence. Simulations were therefore performed to determine the mean distance that an electron travels (in the absence of a magnetic field) before its initial direction (u, v, w = 0, 0, ) is altered by 90 degrees. Figure 4.4 plots the mean distance travelled (in water) by 0., 0.5,, 5, 0, and 5 MeV electrons before their initial trajectory is deviated by a given angle. Figures 4.5 (a), (b), (c), (d), (e), and (f) show the populations of 0., 0.5,, 5, 0, and 5 MeV electrons as functions of the mean distance travelled before their paths are deviated by more than 25.8, 45.6, 60, and 90 degrees (i.e. w = 0.9, 0.7, 0.5, and zero), respectively. 0 Distance electrons travel before deviated by a given angle Mean range (cm) e Angle deviated (degrees) 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Figure 4.4: Distance travelled by electrons before they are deviated from their initial trajectory by a given angle. Simulations were also performed to determine the mean w-values of first generation electrons beyond a depth of 6.9 cm in the water phantom. Figure 4.6 plots the population and mean w-values as a function of energy for first generation electrons of a 5 MV beam beyond 6.9 cm depth. This spectrum is almost identical to that obtained within the entire water phantom in figure 4.3 (a). The main difference between the current spectrum

99 75 Electron population e (a) Path deviation of 0.MeV electrons Distance from origin (cm) 25.8 o 45.6 o 60.0 o 90.0 o Electron population e (b) Path deviation of 0.5MeV electrons Distance from origin (cm) 25.8 o 45.6 o 60.0 o 90.0 o Electron population e (c) Path deviation of MeV electrons Distance from origin (cm) 25.8 o 45.6 o 60.0 o 90.0 o Figure 4.5: Distance electrons travel in water before the angle of deviation from their initial trajectory exceeds 25.8, 45.6, 60, and 90 degrees (i.e. w = 0.9, 0.7, 0.5, and zero). A plot of the accumulative electron population as a function of distance travelled from the origin is shown in figures (a), (b), and (c) for 0., 0.5, and MeV electrons, respectively.

100 76 Electron population e (d) Path deviation of 5MeV electrons Distance from origin (cm) 25.8 o 45.6 o 60.0 o 90.0 o Electron population e (e) Path deviation of 0MeV electrons Distance from origin (cm) 25.8 o 45.6 o 60.0 o 90.0 o Electron population e (f) Path deviation of 5MeV electrons Distance from origin (cm) 25.8 o 45.6 o 60.0 o 90.0 o Figure 4.5: Distance electrons travel in water before the angle of deviation from their initial trajectory exceeds 25.8, 45.6, 60, and 90 degrees (i.e. w = 0.9, 0.7, 0.5, and zero). A plot of the accumulative electron population as a function of distance travelled from the origin is shown in figures (d), (e), and (f) for 5, 0, and 5 MeV electrons, respectively.

101 77 and the former is the inclusion of the w-values between 0. and 0.0 MeV. According to figure 4.6, about 50% electrons have an energy less than 0.5 MeV and w-values less than 0.25 (i.e. less than 76 degrees deviation from the z-axis). The figure also shows that about 30% of electrons have a w-value greater than (i.e. deviated less than 45 degrees), indicating that the dominant component of their range is along the z-axis. e+07 5MV beam: first generation electrons beyond 6.9cm depth Number of electrons e population w-value Energy (MeV) Mean w-value Figure 4.6: Population and mean w-values of first generation electrons for 5 MV beam beyond 6.9 cm depth (in water). According to the secondary electron spectra for a 5 MV beam (figure 4.4), about 40% of secondary electrons have an energy of MeV or higher. As shown in figure 4.6, this corresponds to a w-value greater than 0.8 (beyond 6.9 cm depth), where most of these electrons maintain a w-value above 0.7 over their range (refer to figure 4.5). Lower energy electrons, on the other hand, exhibit substantial alterations in their direction, particularly near the end of their range. Most of these electrons have a w-value below 0.7, which equates to a deviation of more than 45 degrees from their initial direction. It is therefore a combination of larger ranges and w-values that renders the paths of higher energy electrons more susceptible to alteration by the magnetic field.

102 Effect of magnetic field on the spatial distribution of electrons For the path of an electron to be affected by a magnetic field, its cyclotron radius must be comparable to or smaller than its range. For the case of a transverse magnetic field applied along the x-axis, electrons moving perpendicular to the field along the y or z axes will experience the largest deviation, while those moving parallel to the field will be unperturbed. When an electron has a w-value greater than 0.7 (i.e. deviated less than 45 degrees), the dominant component of its range is along the z-axis (i.e. depth direction). According to the secondary electron spectra for a 5 MV photon beam (figure 4.4), this occurs at electron energies of 0.5 MeV or higher. Considering the range of these electrons is comparable to or larger than their cyclotron radii at most magnetic field strengths, their trajectories and depths of interaction will be affected, and so will the spatial distribution of any secondary particles they produce. A detailed examination of how the range and spatial distribution of electrons is affected by the presence of a transverse magnetic field (7 to 9 cm depth) is shown in figures 4.7 to 4.20, where electrons are tracked from five different starting depths within the vicinity of a magnetic field: 6.9, 7.5, 8.5, 8.9, and 9. cm. The study was performed with monoenergetic electron beams of 0.0, 0.05, 0., 0.5,, 5, 0, and 5 MeV subjected to magnetic fields of,.5, 2, 3, 5, 0, 20, 30, 40, 50, 75, and 00 T, where the mean y-range, z-range, and spatial distribution of these electrons as a function of magnetic field strength was investigated for each of the five starting depths. Figure 4.7 shows the mean range and spatial distribution of monoenergetic electrons starting at 6.9 cm depth (immediately before the slice of magnetic field). The depth of interaction of electrons subjected to different magnetic fields is shown in figure 4.7 (a). In the absence of magnetic field, the mean z-ranges of, 5, 0, and 5 MeV electrons were determined to be 0.2,., 2.4, and 3.6 cm respectively. For 5, 0, and 5 MeV electrons, the mean z-range can be seen to decrease to a minimum between 3 and 5 T before recovering to almost its initial value by 00 T. A reduction in mean z- range with increasing magnetic field is also apparent with MeV electrons, although,

103 79 unlike higher energy electrons it does not recover at stronger magnetic fields. The mean depth of interaction of electrons below MeV appears unaltered. Similar trends are exhibited by the ratios of mean z-range with and without a magnetic field in figure 4.7 (b), where a minimum ratio can be seen between 3 and 5 T for 5, 0, and 5 MeV electrons. The plot also reveals a decrease in the ratio with increasing magnetic field for 0.5 and MeV electrons, and ratios of unity are observed for electrons below 0.5 MeV. Figure 4.7 (c) shows the influence of a transverse magnetic field on the depth of interaction of electrons starting at 6.9 cm depth by plotting a ratio of electrons with a final position downstream of their starting position (z > z start ) to those with a final position upstream of the start (z < z start ). For electrons with an energy below MeV, the ratios are constant and greater than unity. At higher electron energies, on the other hand, the ratio decreases with increasing magnetic field and drops below unity between about 5 and 0 T for 5, 0, and 5 MeV electrons. As shown in figure 4.7, an electron s depth of interaction is altered by the magnetic field when its range becomes comparable to or larger than its cyclotron radius. According to figure 3., this occurs at magnetic fields of approximately 2, 0, 20, and 00 T for 0.5, 0., 0.05, and 0.0 MeV electrons respectively. At magnetic fields between and 00 T, electrons with an energy of MeV or higher exhibit variations in their mean z-range as their total range becomes comparable to or larger than their cyclotron radii. Lower energy electrons, on the other hand, exhibit only minor changes in their mean z-range at these magnetic fields as stronger fields are required to sufficiently reduce their radii to values less than or comparable with their ranges. When electrons start at 6.9 cm depth, only those with a z-range greater than 0. cm will reach the magnetic field (between 7 and 9 cm depth). Since MeV electrons have a mean z-range of 0.2 cm, those entering the magnetic field will become trapped unless their radii of curvature is sufficiently smaller than their range to allow escape ( MeV electrons subjected to a 5 T field have a 0. cm radius). The electrons that do escape (via the upstream boundary) have insufficient range to return to their starting depth, which

104 80 Depth of interaction for electrons starting at 6.9cm Mean z-range (cm) (a) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Magnetic field (T) Depth of interaction with and without magnetic field Mean z-range (B/B=0) (b) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Magnetic field (T) Number of electrons (z + / z - ) (c) Ratio of downstream to upstream electrons 0 00 Magnetic field (T) 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Figure 4.7: Magnetic field s influence on the interaction depths of electrons starting at 6.9 cm depth. Figure (a) plots the electrons mean z-ranges as a function of magnetic field. A ratio of the mean z-ranges with and without magnetic field is shown in figure (b), and a ratio of electrons with final positions downstream of their initial position (z > z start ) to those with final positions upstream (z < z start ) is plotted in figure (c).

105 8 Lateral range of electrons starting at 6.9cm depth Mean y-range (cm) 3 2 (d) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Magnetic field (T) Lateral range of electrons with and without magnetic field Mean y-range (B/B=0) (e) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Magnetic field (T) Number of electrons (y - / y + ) (f) Ratio of electrons with negative to positive y-endpoints 0 00 Magnetic field (T) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Figure 4.7: Magnetic field s influence on the lateral ranges of electrons starting at 6.9 cm depth. Figure (d) plots the mean y-ranges of electrons as a function of magnetic field. A ratio of the mean y-ranges with and without magnetic field is shown in figure (e), and a ratio of electrons with negative final y-positions (y < 0) to those with positive final y-positions (y > 0) is plotted in figure (f).

106 82 results in smaller mean z-ranges with increasing magnetic fields. Electrons with an energy of 5 MeV or higher reveal an initial reduction in mean z-range up until about 5 T, at which a minimum z-range is observed. This is attributed to the range of these electrons being sufficiently larger than their radii as to enable their trajectories to be bent upstream by the magnetic field. These electrons therefore have an increased probability of escaping the magnetic field (via the 7 cm boundary), leading to shallower depths of interaction. The magnetic field at which the minimum mean z-range occurs (between 3 and 5 T) is also where the ratio of upstream to downstream electrons drops below unity, which suggests that electrons are depositing their energy in close proximity to their initial position (z start ). When these electrons are subjected to stronger magnetic fields, their smaller radii enable them to escape the field region sooner, resulting in energy depositions further upstream. This upstream migration of electrons gives rise to the increase in mean z-range (beyond the minimum) with increasing magnetic field. The lateral range of electrons is also affected by the presence of a transverse magnetic field. As shown in figure 4.7 (d), electrons with an energy of 5, 0, and 5 MeV exhibit an increase in mean y-range with magnetic fields up to 20 T, where the largest increase of as much as 200% occurs between 2 and 3 T. Beyond 20 T, the mean y-range is approximately constant. For electrons with an energy below 5 MeV, their mean y-range appears unaltered by the presence of a magnetic field. This is demonstrated by ratios of unity for the mean y-range of electrons (below MeV) with and without magnetic field in figure 4.7 (e). However, the ratio for MeV electrons does dip below unity (by as much as 20%) between a magnetic field of 5 and 75 T. A ratio of the number of electrons with a negative y-endpoint (y < 0 cm) to those with a positive y-endpoint (y > 0 cm) is shown in figure 4.7 (f). For electrons with an energy below 0.5 MeV, ratios of unity are observed for all magnetic fields investigated. At greater electron energies of MeV or higher, the ratio exceeds unity, reaching a maximum at 0 T for MeV electrons, 3 T for 5 MeV electrons, and 2 T for 0 and 5 MeV electrons. The magnetic field at which the maximum mean y-range occurs is immediately

107 83 before that at which the minimum z-range occurs, which gives rise to sub-unity ratios of downstream to upstream electrons. The maximum lateral range of electrons corresponds to their mean y-range prior to exiting the magnetic field region (via the 7 cm boundary). Beyond the maximum, the ratio continues to decrease with increasing magnetic field, where it remains above unity as electrons become trapped and thus confined within the field region. Figure 4.8 shows the mean range and spatial distribution of monoenergetic electrons starting at 7.5 cm depth inside the magnetic field. As shown in figure 4.8 (a) and (b), an increase in magnetic field produces a decrease of as much as 95% in the mean depth of interaction (i.e. z-range) of electrons. Generally, the decrease in mean z-range is greater for higher energy electrons except at field strengths below 0 T where the ratios for 0 and 5 MeV electrons are larger than those exhibited by less energetic electrons. Electrons with energies of 0., 0.05, and 0.0 MeV exhibit ratios of approximately unity at magnetic fields up to 0, 20, and 75 T respectively. Figure 4.8 (c) plots a ratio of the electron population with a final position downstream of the start (z > z start ) to that with a final position upstream of the start (z < z start ). The plot reveals ratios greater than unity for all combinations of electron energy and magnetic field. Electrons with energies of 0.5 MeV or higher exhibit a decrease in ratio with increasing magnetic field, while 0., 0.05, and 0.0 MeV electrons exhibit a constant ratio at magnetic fields up to 5, 0, and 50 T respectively. Beyond these fields, the ratio can be seen to decrease towards a minimum at 00 T. At a starting depth of 7.5 cm, electrons with an energy of 5 MeV or lower have insufficient z-range to escape the region of magnetic field via the 9 cm boundary. For more energetic electrons of 0 and 5 MeV, their larger ranges enables them to escape, although at stronger magnetic fields they too become trapped inside the field region. Ratios above unity for electrons with downstream to upstream final positions (relative to their start position, z start ) suggest fewer electrons escape the magnetic field via the magnetic field boundary at 7 cm depth.

108 84 Depth of interaction for electrons starting at 7.5cm Mean z-range (cm) (a) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Magnetic field (T) Depth of interaction with and without magnetic field Mean z-range (B/B=0) (b) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Magnetic field (T) Number of electrons (z + / z - ) (c) Ratio of downstream to upstream electrons 0 00 Magnetic field (T) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Figure 4.8: Magnetic field s influence on the interaction depths of electrons starting at 7.5 cm depth. Figure (a) plots the electrons mean z-ranges as a function of magnetic field. A ratio of the mean z-ranges with and without magnetic field is shown in figure (b), and a ratio of electrons with final positions downstream of their initial position (z > z start ) to those with final positions upstream (z < z start ) is plotted in figure (c).

109 85 Lateral range of electrons starting at 7.5cm depth Mean y-range (cm) 3 2 (d) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Magnetic field (T) Lateral range of electrons with and without magnetic field Mean y-range (B/B=0) (e) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Magnetic field (T) Number of electrons (y - / y + ) (f) Ratio of electrons with negative to positive y-endpoints 0 00 Magnetic field (T) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Figure 4.8: Magnetic field s influence on the lateral ranges of electrons starting at 7.5 cm depth. Figure (d) plots the mean y-ranges of electrons as a function of magnetic field. A ratio of the mean y-ranges with and without magnetic field is shown in figure (e), and a ratio of electrons with negative final y-positions (y < 0) to those with positive final y-positions (y > 0) is plotted in figure (f).

110 86 The magnitude of the electron s lateral range as a function of magnetic field is plotted in figure 4.8 (d). Electrons with an energy of MeV or higher exhibit a maximum mean y-range between about 2 and 3 T. When subjected to stronger magnetic fields, the mean y-range steadily decreases to a minimum value at 00 T, where it is a factor of 0 lower than the maximum. A ratio of the mean y-range obtained with and without magnetic field is plotted in figure 4.8 (e). Electrons with an energy greater than 0. MeV, subjected to magnetic fields of up to 5 T, exhibit mean y-ranges larger than unity by as much as a factor of 2 (for 5 MeV electrons). Between 5 and 0 T, this ratio drops below unity where it steadily decreases towards 00 T. For 0. and 0.05 MeV electrons, the ratio rises above unity from 20 to 75 T and 5 to 50 T, respectively. The mean y-range of the 0.0 MeV electrons is unaffected by the presence of a magnetic field. A ratio of electron population with a negative final y-position (y < 0) to that with a positive final y-position (y > 0) is plotted in figure 4.8 (f), where ratios greater than unity are observed at all electron energies. Generally, the magnetic field at which the maximum ratio occurs is stronger for lower energy electrons. For example, 5 MeV electrons reach a maximum ratio of about 70 at 3 T, while 0.0 MeV electrons exhibit a maximum ratio of around 2 at 00 T. Electrons with an energy of 5 and 0 MeV also exhibit a maximum ratio at 3 T, which is also the field at which their mean z-range becomes less than the.5 cm distance to the downstream field boundary (i.e. electrons become trapped within the magnetic field). Beyond the maximum, the electrons mean y-ranges decrease with increasing magnetic field owing to their smaller cyclotron radii, and hence, confinement within the field. Figure 4.9 shows the mean range and spatial distribution of monoenergetic electrons starting from 8.5 cm depth inside the region of magnetic field. A plot of the depth of interaction, or mean z-range, of electrons as a function of magnetic field is shown in figure 4.9 (a). A ratio of the electrons mean z-ranges with and without the presence of a magnetic field are plotted in figure 4.9 (b). Electrons with an energy of MeV or higher, subjected to magnetic fields less than 2 T, exhibit minor reductions in their mean

111 87 z-range. At stronger magnetic fields, on the other hand, severe reductions in the mean z-ranges of as much as a factor of 3 are observed. This occurs at magnetic fields of about 2, 3, and 5 T for 5, 0 and 5 MeV electrons, respectively, and around T for 0.5 and MeV electrons. For lower energy electrons of 0., 0.05, and 0.0 MeV, a reduction in the ratio can be seen at 5, 0, and 50 T respectively. Figure 4.9 (c) plots a ratio of the population of electrons with a final position downstream of the start (z > z start ) to those with a final position upstream of the start (z < z start ). With the exception of 5, 0, and 5 MeV electrons, these ratios are almost identical to those previously obtained with a start depth of 7.5 cm. The ratios of 5, 0, and 5 MeV electrons subjected to magnetic fields up to 20 T are substantially larger than those observed at 7.5 cm depth, while beyond 20 T they are comparable. For electrons starting at 8.5 cm depth, the distance to the downstream magnetic field boundary is 0.5 cm. This enables electrons with a sufficient range (i.e. 5 MeV energy or higher) to escape the field region and deposit their energy further downstream. Lower energy electrons, on the other hand, remain trapped as they have insufficient z-range to escape. When higher energy electrons are subjected to strong magnetic fields, they too can become trapped within the field owing to their smaller cyclotron radii, particularly when their mean z-range becomes less than 0.5 cm. For 5, 0, and 5 MeV electrons, this occurs at about 3, 0, and 20 T respectively, as indicated by the steep drop-off in their mean z-ranges. For lower energy electrons, the drop-off occurs at stronger magnetic fields, where their ranges become comparable to their radii. Figure 4.9 (d) shows the influence of a magnetic field on the mean lateral range, or y-range, of electrons. For and 5 MeV electrons, a maximum mean y-range occurs at about 3 T, while 0 and 5 MeV electrons exhibit a maximum at 5 and 0 T respectively. At stronger magnetic fields, the mean y-range of these electrons is reduced by as much as a factor of 2. Figure 4.9 (e) plots a ratio of the mean y-range obtained with and without magnetic field. For 5, 0, and 5 MeV electrons, a maximum ratio is observed at about 3, 5, and 0 T respectively, which is immediately before the mean z-range becomes

112 88 Depth of interaction for electrons starting at 8.5cm Mean z-range (cm) (a) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Magnetic field (T) Depth of interaction with and without magnetic field Mean z-range (B/B=0) (b) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Magnetic field (T) Number of electrons (z + / z - ) (c) Ratio of downstream to upstream electrons 0 00 Magnetic field (T) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Figure 4.9: Magnetic field s influence on the interaction depths of electrons starting at 8.5 cm depth. Figure (a) plots the electrons mean z-ranges as a function of magnetic field. A ratio of the mean z-ranges with and without magnetic field is shown in figure (b), and a ratio of electrons with final positions downstream of their initial position (z > z start ) to those with final positions upstream (z < z start ) is plotted in figure (c).

113 89 Lateral range of electrons starting at 8.5cm depth Mean y-range (cm) 3 2 (d) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Magnetic field (T) Lateral range of electrons with and without magnetic field Mean y-range (B/B=0) (e) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Magnetic field (T) Number of electrons (y - / y + ) (f) Ratio of electrons with negative to positive y-endpoints 0 00 Magnetic field (T) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Figure 4.9: Magnetic field s influence on the lateral ranges of electrons starting at 8.5 cm depth. Figure (d) plots the mean y-ranges of electrons as a function of magnetic field. A ratio of the mean y-ranges with and without magnetic field is shown in figure (e), and a ratio of electrons with negative final y-positions (y < 0) to those with positive final y-positions (y > 0) is plotted in figure (f).

114 90 less than 0.5 cm (i.e. distance to the downstream field boundary). At stronger magnetic fields, the electrons cyclotron radii become less than their range, which gives rise to the reduction in their mean y-ranges as the electrons become more confined. Figure 4.9 (f) plots a ratio of the number of electrons with a negative final y- position (y < 0) to those with a positive final y-position (y > 0), where ratios above unity are observed for all electron energies. For 5, 0, and 5 MeV electrons, the ratios peak at about 3, 5, and 0 T respectively, before dropping by factors as large as 40, 50, and 30. For electrons with an energy less than 5 MeV, however, the lower the energy the stronger the magnetic field at which maximum ratio occurs, where a gradual decrease in ratio can be seen beyond the maximum (approaching 00 T). Electrons with an energy less than 0. MeV, on the other hand, exhibit ratios of unity as their mean z-ranges are smaller than their cyclotron radii. Figure 4.20 shows the mean range and spatial distribution of monoenergetic electrons starting at a depth of 8.9 cm (in water) immediately before the downstream magnetic field boundary at 9 cm. The mean z-range of monoenergetic electrons subjected to different magnetic fields is shown in figure 4.20 (a). A ratio of the mean z-range with and without magnetic field is plotted in figure 4.20 (b). A reduction in the mean z-range of electrons occurs at different magnetic fields. For example, electrons with an energy of 5, 0, and 5 MeV exhibit a substantial reduction in mean z-range beyond magnetic fields of about 0, 20, and 30 T respectively. For less energetic electrons, a steady reduction in the mean z-range can be seen beyond T for 0.5 and MeV electrons, and 5, 0, and 50 T for 0., 0.05, and 0.0 MeV electrons, respectively. Figure 4.20 (c) plots a ratio of the electrons with a final z-position downstream of their starting position (z > z start ) to those with a final z-position upstream of the start (z < z start ). Electrons with energies less than MeV exhibit initial ratios of as much as 40, before they steadily decrease toward unity with increasing magnetic field. Similarly, higher energy electrons between and 5 MeV exhibit large ratios of as much as 600 for magnetic fields up to around 0 T, at which their ratio drops rapidly toward unity.

115 9 Depth of interaction for electrons starting at 8.9cm Mean z-range (cm) (a) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Magnetic field (T) Depth of interaction with and without magnetic field Mean z-range (B/B=0) (b) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Magnetic field (T) Number of electrons (z + / z - ) (c) Ratio of downstream to upstream electrons 0 00 Magnetic field (T) 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Figure 4.20: Magnetic field s influence on the interaction depths of electrons starting at 8.9 cm depth. Figure (a) plots the electrons mean z-ranges as a function of magnetic field. A ratio of the mean z-ranges with and without magnetic field is shown in figure (b), and a ratio of electrons with final positions downstream of their initial position (z > z start ) to those with final positions upstream (z < z start ) is plotted in figure (c).

116 92 Lateral range of electrons starting at 8.9cm depth Mean y-range (cm) 3 2 (d) 0.0MeV 0.05MeV 0.MeV 0.5MeV MeV 5MeV 0MeV 5MeV Magnetic field (T) Lateral range of electrons with and without magnetic field Mean y-range (B/B=0) (e) 0 00 Magnetic field (T) Number of electrons (y - / y + ) Ratio of electrons with negative to positive y-endpoints (f) 0 00 Magnetic field (T) Figure 4.20: Magnetic field s influence on the lateral ranges of electrons starting at 8.9 cm depth. Figure (d) plots the mean y-ranges of electrons as a function of magnetic field. A ratio of the mean y-ranges with and without magnetic field is shown in figure (e), and a ratio of electrons with negative final y-positions (y < 0) to those with positive final y-positions (y > 0) is plotted in figure (f).

117 93 For electrons starting at 8.9 cm depth, those with an energy of MeV and higher have sufficient range to exit the magnetic field region via the boundary at 9 cm depth. As these electrons need only traverse a depth of 0. cm to escape, almost no change will be observed in their mean z-range until it becomes comparable with their radii. For, 5, 0, and 5 MeV electrons, this occurs at magnetic fields of about 2, 0, 20, and 30 T respectively. When subjected to stronger magnetic fields, these electrons have radii less than 0. cm, thereby preventing their escape from the field region and producing a severe reduction in mean z-range. The consistent mean z-ranges of electrons with an energy of MeV or lower at all starting depths inside the magnetic field region (i.e. 7.5, 8.5, and 8.9 cm) is due to their confinement within the magnetic field. A maximum mean y-range of electrons is observed around the same magnetic field at which their mean z-range becomes less than the 0. cm distance to the downstream field boundary. The rapid drop-off in mean y-range beyond the maximum is due to the confinement of electrons within the magnetic field as their ranges become comparable with their cyclotron radii. This is confirmed by ratios of unity for electrons with downstream to upstream endpoints with respect to their initial z-position, z start. The effect of a transverse magnetic field on the lateral range of electrons is shown in figure 4.20 (d). The plot reveals an increase in the mean y-range of, 5, 0, and 5 MeV electrons with increasing magnetic field up to 5, 0, 30, and 40 T respectively. According to the ratio of mean y-range with and without magnetic field in figure 4.20 (e), 0.5, 0., 0.05, and 0.0 MeV electrons exhibit a maximum y-range at 5, 20, 50, and 30 T respectively. At field strengths beyond the maximum, the ratio drops below unity for 0. MeV and higher electrons as their smaller cyclotron radii increase their probability of confinement within the magnetic field. In figure 4.20 (f), the ratio of electrons with a negative final y-position (y < 0) to those with a positive y-position (y > 0) is greater than unity for all electron energies. For 5, 0, and 5 MeV electrons, a maximum ratio occurs at magnetic fields of 0, 30, and 40 T respectively. The shift in the maximum ratio to stronger magnetic fields (compared

118 94 with those observed with starting depths of 7.5 and 8.5 cm) is attributed to the smaller cyclotron radii of electrons, and hence, greater confinement of trajectories within the field region. The consistent ratios exhibited by electrons with an energy of MeV and lower at starting depths of 7.5, 8.5, and 8.9 cm, is indicative of their confinement within the magnetic field. 4.4 Conclusion Normalisation of the electron distribution obtained with and without a slice of transverse magnetic field (between 7 and 9 cm depth) accentuated changes in the electron spectrum similar to those observed in the depth-dose profiles of chapter 3. An increase in secondary electron population was observed in the regions approaching and entering the magnetic field (5.5 to 6.5 cm and 6.5 to 7.5 cm depth, respectively), while a decrease in population was exhibited by the regions exiting and beyond the field (8.5 to 9.5 cm and 9.5 to 0.5 cm, respectively). This alteration in population is brought about by a change in the trajectories of electrons whose ranges are comparable to or larger than their radii of curvature. When these electrons are subjected to a transverse magnetic field, their depth of interaction is reduced as well as the depth at which any secondary particles are produced. This upstream migration of electrons gives rise to the augmentation of secondary electron population, and hence, dose enhancement in the regions before and entering the magnetic field. It is also responsible for the depletion of secondary electrons and the corresponding dose reduction beyond the magnetic field, with the exception of first generation electrons (as photon trajectories are unaffected by magnetic fields). The larger maximum and minimum electron populations obtained with field strengths of 5 T or higher, compared with 2 T, are attributed to the electrons smaller radii of curvature, which increase their probability of confinement within the magnetic field. Since the LET of an electron increases with decreasing energy, the redistribution of secondary electrons, particularly low-energy electrons may correspond with a change in the relative biological effectiveness (RBE). This being the case, the augmentation of

119 95 the low-energy electron population in the regions approaching and entering the magnetic field would correspond to an increase in RBE, and conversely, the reduction in low-energy electron population in the regions exiting and beyond the field would correspond to a decrease in RBE. Such an alteration of RBE would benefit the treatment of tumours near radiation-sensitive structures, where the regions of increased and decreased RBE would be aligned with the tumour volume and critical structure respectively. Quantification of the RBE associated with alterations in the secondary electron spectrum is needed to confirm this hypothesis. Replacing the slice of uniform magnetic field with a realistic non-uniform field, such as the field produced by an MRI magnet, is also needed to determine whether the alterations in the electron spectrum associated with the regions of dose enhancement still exist.

120 96

121 CHAPTER 5 MOSFET DOSIMETRY IN MICROBEAM RADIATION THERAPY (MRT) 5. Introduction This chapter explores the performance of edge-on MOSFET dosimeters in Microbeam Radiation Therapy (MRT) with an investigation of their radiation response and ability to measure the dose profiles of monoenergetic and polyenergetic microbeams. The use of MOSFETs to estimate the peak-to-valley dose ratios (PVDRs) of microbeams is also studied. The MOSFET measurements are supplemented with theoretical results obtained by means of Monte Carlo PENELOPE simulations. 5.. Microbeam Radiation Therapy (MRT) Microbeam Radiation Therapy (MRT) is an innovative experimental technique for the treatment of inoperable pediatric brain tumours which offers an alternative to other types of therapy deemed inadequate or unsafe [6, 8, 9, 2 23, 30, 80 82]. Studies have shown that the millimeter-wide X-ray beams used in conventional radiotherapy can be irremediably damaging to a developing brain, especially for children less than three years of age, posing unacceptable risks of long-term neurological disability [5 9]. The advantage of MRT over broad-beam radiotherapy stems from the high tolerance of normal tissue to large amounts of radiation in small volumes, resulting in the preservation of tissue architecture. This was first observed in 967 by Curtis at the Brookhaven National Laboratory (BNL) in a study of the cosmic radiation damage to brain tissue of astronauts [3]. Surrogate mice brains were irradiated with 22 MeV cyclotron-generated deuterons collimated to mm and 25 µm wide beams. Irradiation with a mm wide beam and absorbed doses of 40 Gy obliterated the brain cortex, 97

122 98 while a 25 µm wide beam and an absorbed dose of up to 4000 Gy left the cortex intact. Curtis proposed that this high tissue tolerance of microbeams was related to the regeneration of damaged blood vessels by surviving vasculature endothelial cells in the spaces between microbeams. In the early 990s, with the availability of high intensity synchrotron generated X- ray beams, investigations began into the potential applications of using X-ray microbeams in radiotherapy and radiobiology [32]. The extreme intensity of this electromagnetic radiation (generated from the acceleration of ultra-relativistic charged particles through magnetic fields) led Slatkin et al. to perform a study analogous to that by Curtis almost three decades earlier. Slatkin et al. irradiated normal rat brain tissue with a single microbeam 20 or 37 µm wide and skin-entrance absorbed doses between 32 and 0000 Gy. Like Curtis, they found brain tissue to be highly resistant to radiation. No signs of necrosis were observed with irradiation entrance doses of 5000 Gy, and no signs of brain damage with doses of 32 or 625 Gy [83]. Current research in MRT, performed at the National Synchrotron Light Source (NSLS) at Upton, New York, USA and the European Synchrotron Radiation Facility (ESRF) in Grenoble, France uses a synchrotron and a multislit collimator to produce an array of parallel, rectangular, micron-sized X-ray beams (microbeams) analogous to the parallel panels of open vertical blinds [9 28]. Aimed at the tumour volume, the microbeams interact in tissue delivering a lethal radiation dose to endothelial cells lying directly in their path (i.e. peak regions). Cells lying in the fraction of a millimeter spacing between adjacent microbeams, known as valley regions, receive a superposition of dose contributions from laterally scattered photons and any secondary radiation produced from interactions in tissue. The dose in the valley is substantially smaller than that in the peak. While the underlying radiobiological principle of MRT is not well understood, its effectiveness is believed to be related to the difference in regeneration of the radiationdamaged vasculature in the path of microbeams from the contiguous, minimally irradiated vasculature in the valleys [20, 84]. In normal tissue, the well-preserved vasculature

123 99 in the valley regions ensures the rapid regeneration of directly irradiated blood vessels. In tumour tissue, however, the irreparable damage to blood vessels starves the surviving tumour cells of oxygenated blood, resulting in their death [9, 24, 29, 82]. Over the past decade, numerous pre-clinical MRT studies on small animals have shown the extraordinary radiation tolerance of normal tissue to microscopically thin ionising radiation beams. In the late 990s, Laissue et al. irradiated the cerebella of suckling rats bearing relatively advanced ( 4 mm diameter) malignant tumours to explore the extent and severity of radiation damage with different MRT setups [29]. Irradiation of brain tissue with an array of 0 microbeams (each 25 µm wide and separated by 00 µm) and a skin-entrance dose of up to 32.5 Gy was shown to slow tumour growth and, in more than half of the rats, eliminate it. In a later study, Laissue et al. irradiated the hind brain of young rats with 50 or 50 Gy using two different microbeam spacings (20 µm and 05 µm) to investigate any long-term effects of MRT on their brain development [20]. They found that brain tissue irradiated with 20 µm spacing maintained its normal architecture and showed little or no sign of neurological damage, while tissue irradiated with half the microbeam spacing (05 µm) exhibited greater susceptibility to neurological disability. The greater severity of radiotoxic effects prevalent with the smaller microbeam spacing is attributed to the larger valley dose, where fewer healthy cells survive the irradiation to carry out normal tissue repair. In 200, Laissue et al. used the cerebella of piglets as a surrogate for the human infantile brain to assess MRT s potential for inhibiting the growth of tumours while sparing radiotoxicity to the central nervous system (CNS) [2]. Piglet cerebella were irradiated with an array of microbeams (each 28 µm wide and separated by 20 µm) and doses of up to 625 Gy. Post-irradiation, these piglets were found to mature normally alongside their unirradiated littermates despite the appearance of parallel stripes in their cerebella from the paths of microbeams in the CNS tissue. Within the same year, Dilmanian et al. irradiated embryonic duck brains to model the effects of MRT and broad-beam radiotherapy on the developmental process of a human infantile brain [30]. The embryos were

124 00 irradiated with either an array of MRT microbeams (each 27 µm wide and separated by 00 µm) or a broad-beam ( mm wide) 3 to 4 days prior to hatching. Doses of up to 450 Gy and 8 Gy were used for the MRT and broad-beam regimes respectively. The brain tissue of duck embryos subjected to microbeam irradiation tolerated at least three times more dose than those irradiated with the broad-beam. Small-animal MRT studies have shown that substantial therapeutic or palliative doses of up to several hundred Gy can be administered to cerebella without adverse radiotoxic side-effects. The radiobiological basis for this stems from the rapid repair of normal tissue by minimally irradiated endothelial and glial cells in the valley regions, and the irreparable radiation damage in multiple microscopic segments of the tumour vasculature. It is therefore essential that the valley dose is kept to a minimum to ensure the preservation of normal tissue architecture and sufficient survival of the endothelial cells needed for normal tissue repair. Based on these assumptions, the effectiveness of MRT is determined by the peak-to-valley dose ratio (PVDR), or the ratio of dose in the centre of the peak to that measured at the center of the adjacent valley. The PVDR depends on factors such as the lateral scattering of synchrotron photons and related low-energy secondary electrons; the corresponding spectra of these electrons; the material composition of the interaction medium; and the microbeam collimator design (i.e. width, height, peak separation, and number of microbeams). Generally, a higher PVDR is obtained using narrow microbeams separated by a wide spacing, where the PVDR is higher at the surface than at depth. The PVDR is not uniform across an array of microbeams. It is smaller in the centre of the array than at the edges due to higher accumulative valley dose at the centre of the array from the overlapping dose tails of individual microbeams. A Monte Carlo study by Bräuer-Krisch et al. estimated the PVDR at the centre of an array of 48 microbeams (25 µm wide, 500 µm high, and separated by 20 µm) to be 30% less than at the edge [22]. The PVDR deteriorates with depth due to a greater number of particles experiencing lateral scattering into the valley regions as they undergo interactions within the

125 0 medium. A number of Monte Carlo studies have estimated the PVDR with depth for a variety of X-ray beam energies and MRT configurations [6, 22, 25, 32, 85]. Slatkin et al. used the EGS4 Monte Carlo code to study the PVDR with depth in the centre of an array of 50 microbeams (25 µm wide, 0.3 cm high, and separated by 200 µm) [32]. For beam energies of 00 and 50 kev, the PVDR at 7.5 cm depth (in a human head phantom) was found to be about 60% less than at the surface (0.5 cm depth). Stepanek et al. repeated these PVDR calculations using the PSI version of the Monte Carlo GEANT code, where he found the PVDRs to be 0 to 20 % less [85]. The discrepancy between the PVDRs was attributed to the different electron transport methods used by the two codes (i.e. PSI- GEANT uses single collision transport whereas EGS4 uses condensed history transport). In a later Monte Carlo (PENELOPE) study, Siegbahn et al. showed the deterioration in PVDR with depth is due to a falloff in valley dose which is more gradual than the falloff in peak dose [86]. The deterioration in PVDR with depth has also been shown experimentally. Bräuer- Krisch et al. used an edge-on MOSFET to measure the peak and valley doses, and PVDR, with depth for an array of 48 microbeams (25 µm wide, 500 µm high, and separated by 20 µm) with the polyenergetic ESRF white beam. The measurements were accompanied with Monte Carlo PSI-GEANT simulations. While the absolute dose measurements in the peak and valley were found to be 20% lower than the theoretical values, the PVDRs were within 5% [22]. A study by Orion et al. showed reasonable agreement between a normalised dose profile of a single microbeam measured with a MOSFET dosimeter and simulated with Monte Carlo EGS4 [87]. While the PVDRs of monoenergetic microbeams have been investigated with Monte Carlo [25, 32, 85], absent from the literature are physical measurements of their dose profiles and PVDRs. This chapter compares the dose profiles and PVDRs of monoenergetic microbeams measured with a MOSFET dosimeter and simulated with Monte Carlo PENELOPE.

126 MOSFET dosimetry in MRT An ongoing challenge in MRT is to find a suitable dosimeter that can measure the absolute dose deposition of microbeams with high spatial resolution on a micron scale [25]. Dosimetric systems commonly used in broad-beam radiotherapy, such as ion chambers, thermoluminescence dosimeters (TLDs) and radiochromic films, are unsuitable for microdosimetry. MRT dosimetry has therefore relied on a combination of experimental and theoretical Monte Carlo methods. For MRT dosimetry at the ESRF, radiochromic film is used to provide information about the microbeam profiles, while ion chambers and TLDs are used to perform absolute dose measurements in homogeneous fields greater than cm 2 [25]. Radiochromic film is advantageous in that it has a high spatial resolution of around 600 line pairs per mm [88], which makes it suitable for use in applications involving high dose gradients and relatively high absorbed dose rates such as MRT [89]. The disadvantage of film, however, is that it is unable to provide accurate absolute dose measurement due to the non-linear energy response of the film in the low-energy region of the X-ray spectrum, which is between about 30 and 50 kev [25, 88]. An alternative dosimeter for use in MRT is the Metal-Oxide-Semiconductor Field- Effect Transistor (MOSFET). Its micron, or submicron, sensitive volume allows dosimetric measurements to be performed with high spatial resolution. Currently, it is the only real-time readout dosimeter capable of micron-sized spatial resolution. MOSFET dosimetry was introduced in 974 by A. Holmes-Siedle, who proposed its use as a spacecharge dosimeter [90]. Since then, MOSFET dosimetry has primarily been applied in space dosimetry for monitoring the effects of space radiation on Earth orbiting satellites [9]. In the last decade, however, MOSFET dosimetry has found its way into a number of medical applications ranging from in vivo dosimetry to surface dose measurements, where its use in synchrotron radiation was first investigated in 998 by Kron et al. [92].

127 03 A MOSFET is based on the modulation of charge concentration by a MOS capacitance between a gate and body which are insulated by a gate dielectric layer such as silicon dioxide, SiO 2. Separated by the body region are two individual highly doped regions, called the source and drain, which are both either p or n type and of opposite type to the body region. The inversion layer, or conducting channel, between the source and drain is therefore either of n or p type semiconductor material, and hence, the device is accordingly named a n-mosfet or p-mosfet. Radiation Source (S) Gate (G) SiO 2 Gate oxide Drain (D) p + n p + V S Si Substrate V D Figure 5.: Schematic diagram of a p-mosfet (Metal-Oxide-Semiconductor Field Effect Transistor) dosimeter. In this thesis, MOSFET dosimetry was performed with p-type dosimeters. Figure 5. shows the construction of a p-mosfet, where the source and drain are p + regions and the body is an n region. The operation of a MOSFET is based on the generation of electron-hole pairs by ionising radiation in the gate oxide, where generally the amount of trapped charge is proportional to the energy imparted by the radiation ( 8 ev of energy is required to create an electron-hole pair in SiO 2 ). Applying a negative gate-substrate voltage forces positively charged holes to move towards the Si/SiO 2 interface where they

128 04 become captured by traps in the gate oxide. This build-up of positive charge alters the conductivity in the p-channel, which leads to a change in the gate voltage (i.e. shift in threshold voltage V th ) to ensure a constant current flow through the channel. If the gate voltage is less negative than the (negative) threshold voltage, the channel disappears and only a weak subthreshold current flows between the source and drain. The shift in threshold voltage before and after irradiation is proportional to the absorbed dose in SiO 2 and can be measured by means of a MOSFET reader. A simplified readout circuit of a MOSFET reader is shown in figure V s Current source I D Gate A Source Drain V th = V G measured Figure 5.2: Schematic diagram of the MOSFET reader. The MOSFET dosimeter is read out under a constant current I D with the gate and source grounded. The threshold voltage, V th, measured across the MOSFET is proportional to the dose deposited in the SiO 2 gate oxide. Irradiation of MOSFET dosimeters can be either passive (without a voltage on the gate) or active (positive gate bias voltage). The application of a positive gate voltage reduces the recombination of electron-hole pairs in the SiO 2 gate oxide, which increases the linearity and sensitivity of the MOSFET response. From basic electrostatic principles, the response of a p-mosfet operated in passive and active mode can be approximated by equations 5. and 5.2

129 05 V 2 th (passive) D 0.4 t 2 ox (5.) V 2 th (active) 0.04Dt 2 oxf (5.2) where D is the amount of dose (in Rad) deposited in the gate oxide of thickness t ox (µm), and f is the fraction of holes which escape recombination (this approaches one with increasing positive bias voltage) [93, 94]. When a MOSFET is operated in passive mode, the dose response is sub-linear due to the repulsion by the Coulomb field produced by the trapped holes. In active mode, the dose response is essentially linear over a wide range. The linearity of response depends on the thickness of the oxide layer, electrical field in the oxide, and technology of the oxide growth [95]. The lifetime of a MOSFET is determined by dose limits at which the charge build-up effect saturates in the gate oxide, or the non-linear response becomes intolerable. The small micron-sized sensitive volume and non-destructive readout of MOSFET dosimeters has led to their use in a wide range of radiotherapy applications during the last decade [96]. For most applications involving photon dosimetry, the MOSFET response in tissue-equivalent phantoms is driven by scattered electrons where it follows the Bragg-Gray cavity theory (i.e. number of electrons inside a cavity placed within a medium would also exist in the absence of the cavity). When a MOSFET is used in free-air geometries it, like any silicon device, has an energy dependence. For low-energy photon irradiation, such as the X-ray beam produced by a synchrotron, the MOSFET has been found to exhibit an over-response of dose when compared with tissue/water equivalent detectors [92]. This over-response is shown in figure 5.3 for the Wollongong and T & N MOSFETs, whose response differs because of their packaging materials [97]. The high spatial resolution of the MOSFET dosimeter was fully realised by Rosenfeld et al. who proposed operating the device in what is now called edge-on mode (i.e. orientation of MOSFET chip is such that the interface between its sensitive volume and

130 06 Figure 5.3: The dose response of MOSFET detectors to effective radiation energy. The dose response (in free-air geometry) was normalised to that obtained with 6 MV X-rays from a medical linear accelerator [92]. substrate is parallel with the beam direction) to provide a resolution of µm [98]. Since its inception, edge-on MOSFET dosimetry has received a lot of attention in microdosimetric applications. This chapter explores the MOSFET s suitability for dosimetry in MRT MRT at the ESRF ID-7 biomedical beamline MRT experiments in the present work were conducted at the ID-7 biomedical beamline of the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. The ESRF is a third generation electron synchrotron comprising a 6 GeV evacuated electron storage ring of 844 m circumference. Bunches of electrons orbit in 2.8 µs to produce a maximum ring current of 200 ma, which has a decay time of 50 hours [22]. The ultrarelativistic electrons emerge from storage ring and pass through an alternating magnetic

131 07 field (generated by a wiggler insertion device) to produce synchrotron radiation with a characteristic small source size, high intensity, and a broad continuous spectrum spanning from infrared to X-rays [30]. Tangential to the storage ring is the ID-7 biomedical beamline which services the MRT facility. As illustrated in figure 5.4, it uses a polyenergetic X-ray spectrum (white beam) ranging from about 50 to 350 kev with a maximum intensity of 83 kev and a mean energy of 07 kev [6, 25, 86]. The lower energy photons have been filtered from the beam using.6 cm of aluminium. X-ray energy spectrum for MRT Photon flux (a.u.) Energy (kev) Figure 5.4: X-ray energy spectrum for MRT measured at the ESRF ID-7 biomedical beamline. The filtered white beam emerges from a beryllium window into air and travels through an ionisation chamber before striking a multislit collimator 33 m downstream of the source [22, 23], as shown in figure 5.5. The multislit collimator, which is discussed in more detail in chapter 7, shapes the wide beam into an array of parallel, rectangular, micron-sized X-ray beams (microbeams) for MRT. Exiting the collimator, the microbeams travel through m of air before striking a target which is fixed to the stage of a

132 08 three-axis goniometer device [23]. The Kappa-type goniometer is a computer-controlled device which allows high-resolution rotation and translation of the target in 3-D with respect to the beam. wiggler Be primary X-ray Be window slits filters window MSC goniometer Distance from source (m) Figure 5.5: Schematic diagram of the MRT setup at the ESRF ID-7 beamline. Monoenergetic beams are produced from the insertion of a crystal monochromator device into the path of the polyenergetic synchrotron beam. The crystal diffracts the incident X-ray beam to produce beams at specific angles depending on their wavelength, or energy. The desired beam energy is therefore selected by adjusting the angle of the crystal with respect to the incident beam. Irradiation of the target is performed with either the expose or irradiate method, depending on the nature of the target. The expose method uses a stationary goniometer which is moved into position prior to irradiation of approximately 30 ms duration, which corresponds with the minimum reliable time that the fast shutter is open. Alternatively, the irradiation method is performed by moving the target upwards through the beam at a constant speed. For this method, the goniometer is programmed to move with vertical speed, acceleration, and deceleration to paint a prescribed dose (which takes into account the storage ring current) over a selected volume with millimeter and millisecond precision [22]. The time that each element of the target is exposed to the beam is determined by a fast shutter system [99], which is located upstream from the multislit collimator and Kappa-type goniometer manufactured by Huber, Germany.

133 09 synchronised with the goniometer s vertical translation. Acceleration and deceleration of the goniometer is timed in such a way to provide a constant speed of dose painting during beam delivery. 5.2 Experimental and simulation methods MRT dosimetry was performed with a quadruple MOSFET, also known as a RAD- FET 2. Figure 5.6 shows an image of the REM TOT500 RADFET chip which comprises two low-sensitivity MOSFETs, Q2 and Q3, and two high-sensitivity MOSFETs, Q and Q4, encapsulated in opaque epoxy of less than 2 mm [00]. The difference in sensitivity is attributed to the thickness of the gate oxide, which is 0.5 and 0.9 µm for the low and high-sensitivity MOSFETs, respectively. These high and low-sensitivity MOSFETs will here on be referred to as MOSFET(H) and MOSFET(L) respectively. The RADFET chip was connected to a computerised reader 3, which measured the change in the source to drain voltage required to maintain a source to drain current, I D, of about 60 µa. The RADFET lifetime was limited to a threshold voltage of 27 V, which is the limit of operation of the reader and also the voltage at which the sensitivity of the RADFET significantly changes owing to the accumulation of absorbed dose. The accuracy of the reader was mv and any variation due to background noise was less than 0.5 mv. The experiments were conducted with the synchrotron operating in the four-bunch storage-ring electron-filling mode, which generates a maximum ring current of about 40 ma, which is lower than usual at the ESRF (i.e. 200 ma). The lower current and X-ray flux of this mode reduces the severity of charge-collection saturation and ion recombination effects in MOSFET dosimetry. All irradiations were performed with the expose method. The measured change in MOSFET threshold voltage, or dose response, was normalised to the storage ring current and exposure time. 2 RADFET manufactured by Radiation Experiments and Monitoring (REM), Oxford, UK. 3 Reader developed by the Centre for Medical Radiation Physics, University of Wollongong, Australia.

134 0 0.5 mm Q2 Q Q3 Q4 Figure 5.6: Scanning electron microscope image of the REM TOT500 RADFET chip ( 0.5 mm 3 ), which shows the two low-sensitive MOSFETs, Q2 and Q3, and two high-sensitive MOSFETs, Q and Q4. The direction of the X-ray microbeam is indicated by the arrows [22, 00]. The MOSFET s linearity of radiation response was studied at different threshold voltages for both monoenergetic and polyenergetic beams. The MOSFET(L) and MOS- FET(H) dosimeters were operated in active mode and irradiated under a gate bias voltage of +5 and +5 V respectively, as they provided optimal linearity of threshold voltage versus dose for each RADFET. All measurements were performed with the edge-on MOS- FET at. cm depth in a cylindrical perspex phantom of 2.5 cm diameter and 5 cm depth. The linearity of response to polyenergetic radiation was studied with a MOSFET(H), which had an initial threshold voltage of 8.0 V. In order to reduce the intensity of the white beam, a multislit collimator and aluminium filter were inserted into the beam and the MOSFET was positioned at the centre of a valley region where the beam intensity is lowest. The MOSFET was exposed to 43 pulses of radiation, each with a duration of 0.5 s. After each pulse, the cumulative reader s threshold voltage was recorded and the change in voltage calculated. The linearity of response to monoenergetic radiation was investigated for both the MOSFET(L) and MOSFET(H) dosimeters. The energy of the monoenergetic beam was

135 preselected via the control computer, which changes the beam energy by altering the angle of the crystal monochromator. Measurements were performed using a wide beam configuration (i.e. no multislit collimator and aluminium filter) since monoenergetic beams have a substantially lower intensity than that of the white beam. The radiation response of the MOSFET(L) was investigated with a 50 kev beam. This dosimeter had an initial threshold voltage of 4.6 V and was subjected to 9 pulses of radiation each of 0.03 s duration. The radiation response to 50 and 00 kev beams was investigated with a MOSFET(H). For the 50 kev beam irradiations, the dosimeter had an initial threshold voltage of 24.2 V and was exposed to 9 pulses of radiation each of 0.5 s duration. The same MOSFET(H) was used in an earlier investigation of the radiation response for the 00 kev beam. These measurements were performed with an initial threshold voltage of 22.4 V, and 25 pulses of radiation each of 0 s duration (longer exposures were needed due to the low intensity of the 00 kev beam). MOSFET dosimetry was also used to measure the lateral dose profile of an array of 24 microbeams (each 25 µm wide, µm high, and separated by 42 µm). Dose profiles of individual microbeams were scanned in 2 µm steps with an edge-on MOSFET(L) at. cm depth (in perspex) using the orientation shown in figure 5.7. A dose profile of the central microbeam in the array (peak 2) was obtained for monoenergetic photon beams of 30, 50, 70, and 00 kev. Dose profiles of microbeams 7 and 22 (i.e. 5th and 0th microbeams right of centre when viewing the array from the source position) were also measured for the 50 kev beam. The peak 2 dose profile with the polyenergetic white beam was measured using a MOSFET(H) in the opposite vertical orientation (i.e. mirror image) to that shown in figure 5.7. PVDR estimates were also obtained for all of the aforementioned beams except the 00 kev beam since its low intensity produces large uncertainties in the valley dose. The peak dose of the central microbeam (peak 2) was extracted from the measured dose profiles. The valley dose was measured with the MOSFET at the centre of the valley regions on either side of peak 2 (i.e. ±206 µm), where three to five measurements were

136 2 Perspex phantom 500μm SiO 2 scan direction Si substrate Microbeams Figure 5.7: Illustration of the MOSFET configuration used to scan the dose profiles of monoenergetic microbeams, where the beam direction is into the page. obtained. The PVDR was calculated using the dose at the centre of the peak and an average of the two valley doses on either side. Peak and valley dose measurements, and PVDRs, were also obtained for the 5th and 0th microbeams right of centre (peaks 7 and 22, respectively). MOSFET dosimetry was also used to investigate the variation in PVDR with depth for an array of three microbeams (each 25 µm wide, µm high, and separated by 42 µm) and the white beam. Peak and valley dose measurements were obtained with the edge-on MOSFET positioned at 0.9,.9, and 2.8 cm depth in perspex, and PVDRs were calculated for the central microbeam (peak 2). Monte Carlo PENELOPE simulations were performed to supplement the measured microbeam dose profiles and PVDRs. These simulations incorporated a model of the multislit collimator, synchrotron source, and 34 m source-target distance used for MRT at the ESRF ID-7 beamline (refer to chapter 7 for details). The MOSFET dosimeter was

137 3 not modelled due to its complex geometry and material composition, and also the infeasibility of integrating dose contributions from the different MOSFET positions needed to construct a single dose profile. A lateral dose profile of the full microbeam array was simulated with monoenergetic beams of 30, 50, 70, and 00 kev, as well as the ESRF polyenergetic white beam. Dose was scored between.0 and.2 cm depth (in perspex) for comparison with the profiles measured with a MOSFET at. cm depth. The scoring bins were 2 µm wide (to match the step size used in the MOSFET measurements), 0.2 cm high, and 0.2 cm deep. The electron and photon transport cutoffs were set to kev, and a total of 0 0 primary photon histories were simulated. The PVDRs of individual microbeams were calculated for the different beams using the dose in the central bin of the peak region and an average dose in four bins about the valley midpoint (i.e. ±206 µm from the peak centre). Additional simulations were performed for each beam energy to determine the dose distribution of a single microbeam according to the type of initial photon interaction (i.e. Rayleigh scattering, photoelectric effect, or Compton scattering). These simulations used the PENELOPE variable ICOL, which describes the type of event that has been simulated (i.e. ICOL =, 2, or 3 corresponds to a Rayleigh scattering, Compton scattering, and photoelectric interaction, respectively). Following the initial interaction of a primary photon, the PENELOPE ILB(5) label, which is transferred to all descendants of a primary particle, was set to the value of ICOL. Hence, dose contributions from any descendant particles were tallied according to the type of initial interaction experienced by the primary photon. The dose was scored at. cm depth (in perspex) in bin volumes of cm 3 (width height depth). A total of 0 9 primary photon histories were simulated using photon and electron transport cutoffs of 0.5 and kev respectively. Also simulated was the dose profile of an array of three microbeams at depths of 0.9,.9, and 2.8 cm to compare with the measured profiles. The bin volumes, energy cutoffs and total number of histories were identical to those used in the above simulations

138 4 for an array of 24 microbeams. The PVDR for the central microbeam (peak 2) was calculated using the dose scored in the central bin of the peak and an average of the dose in four bins about the valley midpoint (i.e. ±206 µm from peak centre). Additional simulations were performed to obtain the lateral dose profile, and hence PVDR, at 0., 0.2, 0.3, 0.5, 0.7,., and.2 cm depth in perspex. 5.3 Results and discussion 5.3. Radiation response of MOSFET dosimeters Figure 5.8 (a) shows the response of a MOSFET(H) dosimeter to polyenergetic white beam irradiation, normalised to the synchrotron storage ring current and exposure time. The normalised response of a MOSFET(L) dosimeter to 50 kev monoenergetic beam irradiation is shown in figure 5.8 (b). Figures 5.8 (c) and (d) plot the normalised radiation response of a MOSFET(H) to 50 and 00 kev beams, respectively. The MOSFET(H) dosimeter exhibited a 2% falloff in response when subjected to polyenergetic white beam irradiation and operated between threshold voltages of 8 and 9.8 V (i.e. 7% per Volt). When exposed to monoenergetic radiation of 50 and 00 kev, it exhibited a 5% falloff in response over a.2 V range (i.e. 4% per Volt). The MOSFET(L) dosimeter, on the other hand, experienced a falloff of less than 2% when it was exposed to 50 kev radiation and operated at threshold voltages between 4.6 and 5.2 V (i.e. 3% per Volt). The smaller falloff in radiation response exhibited by the MOSFET(L) dosimeter is attributed to its thinner gate oxide and higher gate bias voltage (i.e. stronger external electric field), which reduces the effect of accumulated positive charge. MOSFET(H) dosimeters, on the other hand, have a thicker gate oxide and therefore reach saturation sooner (at lower doses). The larger falloff in response exhibited by the MOSFET(H) subjected to polyenergetic radiation (than with 50 or 00 kev monoenergetic radiation) is due to the higher intensity of the white beam, causing saturation to occur sooner.

139 5.4 (a) MOSFET(H) response at 8.0V with a white beam Relative response Voltage (V).4 (b) MOSFET(L) response at 4.6V with a 50keV beam Relative response Voltage (V) Figure 5.8: Radiation response of MOSFET dosimeters. Figure (a) plots the normalised response of a MOSFET(H) dosimeter subjected to s pulses of white beam radiation. The response of a MOSFET(L) dosimeter to s irradiations with a 50 kev beam is shown in figure (b).

140 6.4 (c) MOSFET(H) response at 24.2V with a 50keV beam Relative response Voltage (V).4 (d) MOSFET(H) response at 22.4V with a 00keV beam Relative response Voltage (V) Figure 5.8: Radiation response of MOSFET dosimeters. Figure (c) plots the normalised response of a MOSFET(H) dosimeter subjected to s pulses of irradiation with a 50 kev beam. The response of a MOSFET(H) dosimeter to 25 0 s irradiations with a 00 kev beam is shown in figure (d).

141 Measured and simulated dose profiles of microbeams A MOSFET dosimeter was used to measure the lateral dose profile of the central peak in an array of 24 microbeams (peak 2) for monoenergetic beams of 30, 50, 70, and 00 kev, and the polyenergetic ESRF white beam. Figures 5.9 (a), (b), (c), and (d) plot the peak 2 dose profile measured with a MOSFET(L) dosimeter for monoenergetic beams of 30, 50, 70, and 00 kev respectively. The peak 2 dose profile for the polyenergetic white beam which was measured with a MOSFET(H) dosimeter is shown in figure 5.0. Figure 5. compares the measured dose profiles of peak 2 obtained for the different beam energies, where only one scan (scan ) is shown for each energy. The full-width at half-maximum (FWHM) of the 70 and 00 kev monoenergetic profiles was approximately the same. The FWHM of the 30 and 50 kev profiles, on the other hand, were about 3 µm and 2 µm smaller than those obtained with the 70 and 00 kev beams. Common to all monoenergetic profiles was an asymmetry about the peak centre, where the right penumbral dose was smaller than the left penumbral dose. This asymmetry was also observed in the dose profiles of peaks 7 and 22 (i.e. 5th and 0th microbeams right of centre when viewing the array from the source position) obtained with a 50 kev beam. The peak 2 profiles obtained with the white beam also exhibited asymmetry, however, it was an inverse of those observed in the monoenergetic profiles (i.e. the right penumbral dose was higher than the dose in the left penumbra). The asymmetric profiles of measured microbeams prompted Monte Carlo simulation of the lateral dose profile of an array of 24 microbeams (each 25 µm wide, µm high, and separated by 42 µm). Figure 5.2 shows the simulated dose profile of the central microbeam in the array (peak 2) obtained with the white beam and monoenergetic beams of 30, 50, 70, and 00 kev. The dose profile of a single microbeam (25 µm wide and µm high) was also simulated for each beam energy for comparison with the peak 2 profile. A comparison of the penumbral and valley doses of the two microbeam profiles is shown in figure 5.3. Comparison of the measured dose profiles in figure 5. with the simulated dose

142 8 MOSFET relative response keV beam: central microbeam (peak 2) (a) scan scan Position (µm) MOSFET relative response keV beam: central microbeam (peak 2) (b) scan scan Position (µm) Figure 5.9: Dose profiles of monoenergetic microbeams measured at. cm depth (in perspex) with a MOSFET(L) dosimeter. Figures (a) and (b) show the dose profile of the central peak in an array of 24 microbeams (peak 2) for 30 and 50 kev beams, respectively.

143 9 MOSFET relative response keV beam: central microbeam (peak 2) (c) scan scan 2 scan Position (µm) 00keV beam: central microbeam (peak 2) MOSFET relative response (d) scan scan 2 scan Position (µm) Figure 5.9: Dose profiles of monoenergetic microbeams measured at. cm depth (in perspex) with a MOSFET(L) dosimeter. Figures (c) and (d) show the dose profile of the central peak in an array of 24 microbeams (peak 2) for 70 and 00 kev beams, respectively.

144 20 MOSFET relative response White beam: central microbeam (peak 2) scan scan Position (µm) Figure 5.0: Dose profile of the central peak in an array of 24 microbeams (peak 2) obtained with the ESRF white beam and measured with a MOSFET(H) dosimeter at. cm depth (in perspex). profiles in figure 5.2 reveals differences in their shape and FWHM. The measured profiles exhibit higher penumbral doses and an asymmetry about the peak centre which is not apparent in simulated profiles. In addition, the FWHM of the measured profiles varies by up to 3 µm, while for simulated profiles it is approximately the same. Despite these differences, both the measured and simulated 30 kev microbeam profiles exhibit narrower peak doses than profiles obtained with higher energy beams. Beyond the edge of the microbeam (i.e. below the FWHM), the simulated profiles exhibit distinct differences in the penumbral dose, which suggests the FWHM is not a good measure of the changes in the beam profile with energy. The variation in penumbral dose exhibited by simulated microbeam profiles of different energies can be explained by the range of scattered photons and electrons. For the case of a single microbeam in figure 5.3 (a), the distance from the peak at which the valley dose begins to level out corresponds to approximately the maximum range of photoelectrons in perspex. According to figure 5.5, this is about 5, 40, 70, and 20 µm

145 2 MOSFET relative response Measured dose profile of the central microbeam (peak 2) white beam 30keV 50keV 70keV 00keV Position (µm) Figure 5.: Comparison of the dose profile of the central peak in an array of 24 microbeams (peak 2) measured with a MOSFET at. cm depth (in perspex) for the white beam and monoenergetic beams of 30, 50, 70, and 00 kev. for 30, 50, 70, and 00 kev electrons respectively. This is also indicated in the simulation results of figure 5.4, which shows the dose distribution of a single microbeam according to the type of initial photon interaction (i.e. Rayleigh scattering, photoelectric effect, or Compton scattering). For all beam energies, initial photoelectric interactions are primarily responsible for the penumbral dose extending over a distance approximately equal to the maximum range of photoelectrons (in perspex). Beyond this distance, most of the dose contribution is from primary photons undergoing Compton scattering, or to a smaller degree, Rayleigh scattering (whose cross section increases with decreasing energy). The higher valley dose exhibited by peak 2 than by the single microbeam (refer to figure 5.3) is due to the superposition of overlapping valley dose tails of neighbouring microbeams within the array. Inside the peak region, most of the dose is from primary photons undergoing photoelectric or Compton scattering interactions. For the 30 kev beam, peak dose contributions are primarily from photoelectric interactions owing to its larger cross section at this energy. At higher beam energies of 50, 70 and 00 kev,

146 22 Simulated dose profile of the central microbeam (peak 2) 0.8 white beam 30keV 50keV 70keV 00keV (D/D max ) Distance (µm) Figure 5.2: Simulated dose profile of the central microbeam in an array of 24 microbeams (peak 2) obtained at. cm depth (in perspex) for the white beam and monoenergetic beams of 30, 50, 70, and 00 kev. however, most of the peak dose arises from Compton scattering as it is the dominant interaction mechanism at these energies. The lower valley dose exhibited by higher energy beams is due to the larger range of scattered photons, which enables some to contribute to neighbouring microbeams. The simulated profiles do not exhibit the asymmetry observed in measured profiles. Considering the simulations were performed without a model of the MOSFET (i.e. its material composition was identical to that of the phantom), the asymmetry of the measured profiles is related to the construction and composition of the edge-on MOSFET. As shown in figure 5.7, the MOSFET comprises a micron-sized SiO 2 sensitive volume (< µm thick) positioned on top of a silicon substrate which is 500 µm wide and 000 µm high. The MOSFET orientation used to scan the monoenergetic profiles from left to right was such that the sensitive volume led the silicon substrate. Since the height and peak-topeak separation of microbeams were µm and 42 µm respectively, the width of the MOSFET s substrate was able to span an entire peak and adjacent valley region. Hence,

147 23 Dose profile of a single microbeam (D/D max ) (a) white beam 30keV 50keV 70keV 00keV Distance (µm) Dose profile of the central microbeam (peak 2) (D/D max ) (b) white beam 30keV 50keV 70keV 00keV Distance (µm) Figure 5.3: Simulated penumbral and valley dose of a single microbeam, and the central microbeam (peak 2) in an array of 24 microbeams. Figures (a) and (b) plot the dose profile of a single microbeam and peak 2, respectively, at. cm depth (in perspex) for the white beam and monoenergetic beams of 30, 50, 70, and 00 kev.

148 24 30keV: Dose distribution according to initial photon interaction Dose (D/D max ) e-05 (a) Rayleigh Photoelectric Compton Total e Distance (µm) 50keV: Dose distribution according to initial photon interaction Dose (D/D max ) e-05 (b) Rayleigh Photoelectric Compton Total e Distance (µm) Figure 5.4: Simulated microbeam profile showing the dose distribution according to the type of initial photon interaction. Figures (a) and (b) plot the dose contributions of a single microbeam at. cm depth (in perspex) for monoenergetic beams of 30 and 50 kev, respectively.

149 25 70keV: Dose distribution according to initial photon interaction Dose (D/D max ) e-05 (c) Rayleigh Photoelectric Compton Total e Distance (µm) 00keV: Dose distribution according to initial photon interaction Dose (D/D max ) e-05 (d) Rayleigh Photoelectric Compton Total e Distance (µm) Figure 5.4: Simulated microbeam profile showing the dose distribution according to the type of initial photon interaction. Figures (c) and (d) plot the dose contributions of a single microbeam at. cm depth (in perspex) for monoenergetic beams of 70 and 00 kev, respectively.

150 26 when its sensitive volume was centred on a given peak, the substrate covered both the adjacent valley and peak regions to the left. Similarly, when the sensitive volume was positioned in the middle of the right valley region of a given peak, the substrate covered both the peak and valley regions to the left. 000 Silicon Perspex CSDA range of electrons Range (µm) Energy (kev) Figure 5.5: Comparison of the Continuous Slowing Down Approximation (CSDA) range of electrons in silicon and perspex [0]. The obscuration of microbeams by the silicon substrate would not present a problem if the photon and electron mass attenuation coefficients in silicon and perspex were equivalent. However, according to figure 5.5, the Continuous Slowing Down Approximation (CSDA) range of up to 300 kev electrons is about 40% lower in silicon than it is in perspex. For example, a 50 kev electron has a range of about 24 µm in silicon compared with 37 µm in perspex. Consequently, electrons traversing the silicon experience a higher mass energy attenuation coefficient than they would in perspex, resulting in fewer electrons reaching the sensitive volume. Photons of these energies, on the other hand, have longer ranges of the order of millimeters, and are hence less affected by the difference in mass attenuation coefficients. Considering the valley dose is primarily comprised

151 27 of scattered photons and electrons from the proximal peaks, fewer contributions from the left peak will reach the sensitive volume due to attenuation in the silicon substrate. This underestimation of dose is more apparent when the sensitive volume moves into the right penumbra of the peak (i.e. substrate covers the peak), since fewer photoelectrons reach the sensitive volume for detection. The same dose underestimation does not occur in the left penumbra as here the substrate obscures not the immediate peak, but the valley and peak regions to the left where dose contributions are substantially less. The profiles obtained with the polyenergetic white beam exhibit an asymmetry that is the mirror of that observed in the monoenergetic profiles (i.e. lower dose in the left penumbral dose than in the right penumbra). This is because these profiles were scanned with the edge-on MOSFET rotated 80 degrees in the plane perpendicular to the beam, such that the silicon substrate led the sensitive volume. Particle attenuation in the substrate was more severe with lower energy beams, where the FWHM of the 30 and 50 kev profiles were about 3 µm and 2 µm smaller than those obtained with 70 and 00 kev beams. According to the theoretical profiles in figure 5.2, these FWHM should be approximately equal apart from the 50 kev profile which is about µm larger. Since the photoelectric effect is the dominant photon interaction process in silicon below about 60 kev (refer to figure 5.6), the 3 µm difference between the measured and theoretical 30 and 50 kev FWHM arises from the higher absorption of photoelectrons in the substrate prior to reaching the sensitive volume (where the range of a 60 kev electron is about 30 µm) Measured and simulated peak-to-valley dose ratios (PVDRs) Figure 5.7 shows the measured peak-to-valley dose ratio (PVDR) of the central microbeam (peak 2) obtained with monoenergetic beams of 30, 50, and 70 kev, and the polyenergetic white beam. The PVDRs of monoenergetic microbeams increased with increasing beam energy, where PVDRs of around 320, 400, and 460 were calculated for the 30, 50, and 70 kev beams respectively. The PVDR of the white beam, on the

152 28 Cross section (cm -2 ) Photon interaction cross sections in silicon Total cross section Rayleigh scattering Compton scattering Photoelectric effect Energy (kev) Figure 5.6: Photon interaction cross sections in silicon [36]. other hand, was substantially lower than that of the monoenergetic beams. According to the theoretical profiles in figure 5.3, the reduction in valley dose with increasing beam energy suggests the PVDR of the white beam (maximum intensity of 83 kev) should be higher than the PVDRs of the monoenergetic beams. This is shown in figure 5.8 with a comparison of the simulated PVDRs for different beam energies, where the PVDR increases with increasing beam energy. For all beam energies, the measured PVDRs were lower than the theoretical values. For 30, 50, and 70 kev monoenergetic beams, the measured PVDRs were 46, 5, and 2% lower than the simulated values, while for the polyenergetic white beam the difference was more than a factor of two. The measured monoenergetic profiles also show an increase in PVDR between 30 and 50 kev which is not apparent in the corresponding simulated profiles. The PVDRs of the 30 and 50 kev theoretical profiles are almost identical, owing to their similar normalised valley doses. The variation between the 30, 50, and 70 kev measured PVDRs is attributed not only to the different absorption cross sections of silicon and perspex as mentioned above,

153 PVDR of peak 2 obtained with a MOSFET 400 PVDR Energy (kev) Figure 5.7: Measured PVDR of the central microbeam in an array of 24 (peak 2) calculated from peak and valley doses obtained at. cm depth (in perspex) for 30, 50, and 70 kev beams and the white beam (maximum intensity of 83 kev). but also to a dose over-response of the MOSFET. As shown in figure 5.3, MOSFET dosimeters exhibit an overestimation of dose for photon energies up to a few hundred kev [92]. For the T&N MOSFET, which is similar in design to the quadruple MOSFET used for MRT dosimetry in this thesis, the dose over-response occurs between about 30 and 200 kev, reaching a maximum of a factor of 3 at around 50 kev. Although the overresponse occurs in both peak and valley regions, a larger effect can be seen in the peak owing to the higher photon fluence. As shown in figure 5., the effect of attenuation of electrons in the silicon substrate is greater for lower-energy beams due to the shorter range of electrons. Hence, the underestimation of peak dose and PVDR is greater for the 30 kev beam than for the higher energy beams. It is a combination of the MOSFET s over-response and attenuation of low-energy electrons in the silicon substrate that results in the larger PVDRs obtained with 50 and 70 kev beams. These factors, however, do not account for the underestimation of the PVDR measured for the white beam profiles. Considering the intensity of the white beam

154 Simulated PVDR of peak 2 with different beams 800 PVDR Energy (kev) Figure 5.8: Simulated PVDR of the central microbeam in an array of 24 (peak 2) calculated from the theoretical dose profiles at. cm depth (in perspex) for 30, 50, 70, and 00 kev beams and the white beam (maximum intensity of 83 kev). is substantially greater than those of monoenergetic beams, the underestimation of PVDR may be attributed to an under-response of peak dose caused by electric field screening (i.e. damping of electric fields by the presence of mobile charge carriers). This effect, which is known to occur in semiconductor materials exposed to intense electric fields, or high dose rates, increases the recombination of electron-hole pairs, thereby reducing the charge build-up in the gate oxide. One could further investigate this effect by measuring the dose response of the MOSFET in a peak region for different synchrotron storage-ring currents. The fact that simulated PVDRs were higher than their measured counterparts may also be attributed to the simplified modelling of the MOSFET dosimeter whose composition was perspex (i.e. same material as the phantom) and sensitive volume was comparable to that of the scoring bins ( cm 3 ). Hence, the simulations did not account for the attenuation of electrons in the silicon substrate, nor the dose overresponse which is characteristic of MOSFETs used at these photon energies. A Monte

155 3 Carlo study by De Felici et al. showed that modelling silicon detectors at depths of less than 2 cm in PMMA can yield up to 20% larger PVDRs than those obtained without a MOSFET model [6]. The higher simulated PVDRs may also relate to the use of scoring bins that were larger than the MOSFET s sensitive volume. This was done to ensure sufficient dose in valley regions, where little variation in the PVDR should arise as dose is integrated over the full height of the microbeam. It is also possible that the absence of beam polarisation models in the PENELOPE code may have introduced anomalies in the simulated valley dose since it neglects any alterations in dose distribution of scattered photoelectrons from polarised X-rays. A comparison of measured and simulated PVDRs was also investigated for peaks 7 and 22 (i.e. 5th and 0th microbeams right of peak 2 when viewing the array from the source position). Figure 5.9 plots the measured PVDRs for peaks 2, 7, and 22 obtained with a 50 kev beam and polyenergetic white beam. Both the 50 kev and white beam measured profiles exhibit an increase in PVDR with increasing microbeam number from the centre of the array (peak 2). For the 50 kev beam, the measured PVDRs of peaks 7 and 22 are about 5 and 25% larger than that of peak 2. A similar relationship is observed with the white beam, where the PVDRs of peaks 7 and 22 are around 25 and 30% larger than that of peak 2. This increase in PVDR for microbeams further from the centre of the array is commonly observed in MRT. It is brought about by the higher accumulative valley dose at the centre of the array from the superposition of overlapping dose tails of neighbouring microbeams. Since the valley dose has been shown to increase with decreasing beam energy (refer to figure 5.3), one would expect the PVDRs obtained with the white beam to be larger than those obtained with a 50 kev beam. This can be seen in figure 5.20, which plots the simulated PVDRs for an array of 24 microbeams for the 50 kev and white beams. Figure 5.2 plots the PVDRs of individual peaks within the array for different beam energies. As observed with measured profiles, the PVDRs of simulated profiles also increase

156 white 50keV Measured PVDRs for an array of microbeams PVDR Microbeam number Figure 5.9: Measured PVDRs of microbeams 2, 7, and 22 (in an array of 24 microbeams) for the 50 kev and white beams, calculated from peak and valley dose measurements obtained with a MOSFET at. cm depth (in perspex). for microbeams further from the centre of the array. This is due to the lower accumulative valley dose from overlapping dose tails of neighbouring microbeams at the edges of the array. The substantially larger PVDRs exhibited by the last two microbeams at either edge of the array suggest that valley dose contributions are significant only over two or three neighbouring microbeams. For the 50 kev beam, the measured and simulated PVDRs agree within uncertainties (i.e. within the variance of measured PVDRs, and ±3% and ±0% uncertainties in the peak and valley doses of simulated profiles, respectively). For the white beam, on the other hand, a substantial difference exists between the measured and simulated PVDRs, which is well outside the uncertainties. The difference may be attributed to electric field screening effects (mentioned above), which are characteristic of intense radiation. To a lesser extent, it may also stem from simplifications made in the model of the MOSFET dosimeter. Measurements were also performed to investigate the PVDR at different depths in a

157 white 50keV meas 50keV Simulated PVDRs for an array of microbeams PVDR Microbeam number Figure 5.20: Simulated PVDRs of microbeams 2, 7, and 22 (in an array of 24 microbeams) for the 50 kev and white beams, calculated from the theoretical dose profiles obtained at. cm depth (in perspex). The 50 kev measured PVDRs (meas 50 kev) are also shown for comparison. perspex phantom. This study used a MOSFET dosimeter to measure the peak and valley dose of an array of three microbeams (each 25 µm wide, µm high, and separated by 42 µm) at 0.9,.9, and 2.8 cm depths in perspex. Several peak and valley dose measurements were performed about the midpoint of the central peak (peak 2) and the valley regions on either side. All measurements were normalised to both the storage ring current and exposure time. Figure 5.22 compares the measured and simulated PVDRs with depth in perspex for the array of three microbeams. The PVDR of the central microbeam (peak 2) was calculated using the peak dose and an average of the two valley doses on either side. While both measured and simulated profiles exhibited a decrease in the PVDR with increasing depth, the measured PVDRs were about 30% lower than those obtained from simulation. The difference between the measured and simulated results stems from the absence of modelling the silicon substrate and over-response of the MOSFET dosimeter.

158 34 PVDR Simulated PVDRs for an array of microbeams white 30keV 50keV 70keV 00keV Microbeam number Figure 5.2: Simulated PVDRs for an array of 24 microbeams, calculated from the theoretical dose profiles obtained at. cm depth (in perspex) with the white beam and 30, 50, 70, and 00 kev monoenergetic beams. Measured and simulated PVDRs with depth PVDR Simulated Measured Depth (cm) Figure 5.22: Measured and simulated PVDRs with depth (in perspex) for the central peak in an array of three microbeams (peak 2) produced with a white beam. The measured PVDRs were obtained at 0.9,.9, and 2.8 cm depth, and the theoretical PVDRs at various depths up to.2 cm.

159 35. Simulated peak and valley doses with depth Peak Valley Dose (D/D max ) Depth (cm) Figure 5.23: Simulated peak and valley doses for the central peak in an array of three microbeams (peak 2) up to 2.8 cm depth (in perspex). Peak and valley doses have been normalised to their maximum values. The variation in PVDR with depth can be understood by examining the behaviour of peak and valley dose of the central microbeam (peak 2), which is plotted as a function of depth in figure Both peak and valley doses have been normalised to their respective maximum values. The steady decrease in peak dose with increasing depth arises from the attenuation of photons. The initial increase in valley dose is from scattered photons and electron contributions, where beyond a depth of about 0.3 cm the valley can be seen to decrease with increasing depth. As the peak dose decreases with depth at a faster rate than the valley dose, so too does the PVDR. The higher PVDRs near the surface of the phantom are attributed to less photon attenuation in the peak and fewer scattered particles in the valley. These observations are consistent with the Monte Carlo simulation results obtained by Siegbahn et al. [25].

160 Conclusion The falloff in linearity of radiation response of the MOSFET(L) dosimeter was less than that for the MOSFET(H) dosimeter. This is due to its thinner gate oxide and higher gate bias voltage (i.e. stronger external electric field), which reduces the effect of accumulated positive charge. The MOSFET(H) dosimeter, on the other hand, has a thicker gate oxide and therefore reaches saturation sooner (i.e. at lower doses). The larger falloff in response observed with the polyenergetic radiation when compared with monoenergetic beams is due to the higher intensity of the white beam. The measured and simulated dose profiles exhibited differences in their shape and FWHM. Common to all measured profiles was an asymmetry about the peak centre which was not observed in the simulated microbeams. The difference in the left and right penumbral dose arises from the asymmetrical construction of the edge-on MOS- FET, where the µm wide sensitive volume is positioned on top of a 500 µm wide silicon substrate. As silicon has a higher mass attenuation coefficient than perspex, particles travelling through the substrate towards the sensitive volume are attenuated more than particles not obscured by the substrate. This leads to an underestimation of dose from short-range particles, such as low-energy electrons, which are absorbed in the substrate prior to reaching the sensitive volume for detection. This is particularly apparent when the substrate covers the peak region of a given microbeam (i.e. the sensitive volume is in the right penumbra), as here there exists a large population of short-range photoelectrons. The measured dose profiles also exhibited a variation in FWHM with energy which was not observed in the corresponding simulated profiles. The FWHM of the 30 and 50 kev measured profiles were 3 µm smaller that the FWHM obtained with higher energy beams. This difference stems from the asymmetrical penumbral doses caused by particle attenuation in the silicon substrate, which was more apparent for the 30 and 50 kev profiles owing to the shorter ranges of particles). The lower PVDRs for measured profiles relative to theoretical PVDRs were attributed to a combination of physical effects in MOSFET dosimetry and simplifications

161 37 in MOSFET modelling. While the simulated PVDRs for the 30 and 50 kev beams were approximately the same, the measured PVDRs exhibited a 25% increase between the two energies. For the measured 30 kev profile, the underestimation of peak dose and PVDR was due to particle attenuation in the silicon substrate. This was more apparent in the profiles of lower energy beams owing to the shorter ranges of particles, especially photoelectrons. The larger PVDRs of the 50 and 70 kev measured profiles can be attributed to the MOSFET s over-response to photons of these energies. Substantially smaller PVDRs were obtained for the white beam measured profiles than their simulated PVDRs due to an underestimation of peak dose caused by electric field screening and a simplified MOSFET model (comprised of perspex rather than silicon and SiO 2 materials). Hence, the simulations did not account for any particle attenuation in the silicon substrate or over-response of the MOSFET, both of which are characteristic at these photon energies. The absence of beam polarisation models in PENELOPE may have also had an effect on the simulated valley dose by not accounting for the altered dose distribution of scattered photoelectrons from polarised X-rays. Both the measured and simulated PVDRs were found to increase toward the edges of the array. This is due to a higher accumulative valley dose at the centre of the array caused by overlapping dose tails of neighbouring microbeams. For the 50 kev profiles, the measured and simulated PVDRs for peaks 2, 7, and 22 in the array agreed within uncertainty. The corresponding PVDRs obtained with the white beam, however, exhibited a substantial difference between measured and simulated values. The smaller PVDRs obtained for the measured profiles were due to an underestimation of peak dose caused by electric field screening and simplifications of MOSFET modelling. A reduction in PVDR with increasing depth was also observed for the measured and theoretical profiles. Simulations of the peak and valley dose with depth, revealed a reduction in the peak dose owing to photon attenuation. The reduction in peak dose was faster than that in the valley, resulting in smaller PVDRs with increasing depth. The higher PVDRs at shallower depths was therefore due to less photon attenuation in the

162 38 peak and fewer scattered particles in the valley. Despite the drawbacks of particle attenuation and dose over-response, the edge-on MOSFET remains the only real-time dosimeter capable of micron, or sub-micron, resolution. With advances in technology, the feasibility of reducing the 500 µm width of the silicon substrate to minimise particle attenuation will soon be realised. The use of a thinner substrate and an appropriate calibration curve (to correct for MOSFET response as a function of photon beam energy and dose rate) may improve the viability of MOSFET dosimetry in MRT. An alternative real-time dosimeter for use in MRT is the silicon strip detector 4. This device will be used to measure the peak and valley doses for individual microbeams in an array, as well as the instantaneous PVDR for an entire microbeam array. It comprises 28 strips of p + p-n junctions (each 20 µm wide, 500 µm high, and spaced 200 µm apart) bound to a 375 µm thick n-type silicon substrate. The detector will also be used to instantaneously trigger beam stoppage in the event that an undesirable dose is administered to a patient undergoing MRT, where treatment times are in the order of milliseconds. 4 The silicon strip detector is currently under development at the Centre for Medical Radiation Physics at the University of Wollongong, Australia.

163 CHAPTER 6 MAGNETO-MRT: INFLUENCE OF A MAGNETIC FIELD ON MICROBEAM PROFILES 6. Introduction This chapter investigates the potential for the application of magnetic fields in Microbeam Radiation Therapy (MRT), or magneto-mrt, to alter the dose profiles of microbeams and hence the effectiveness of the treatment. Minimising valley dose in order to increase the survival of normal cells needed for tissue repair is an ongoing challenge in MRT. The valley dose comprises a superposition of energy depositions from electrons and photons that laterally scatter from peak regions. As shown in figure 6., a large component of the valley dose is produced by scattered secondary electrons [25]. In chapter 4, the application of transverse magnetic fields to high-energy photon beams was shown to alter the distribution of low-energy electrons (less than MeV for a 5 MV beam). This alteration was brought about by a change in the trajectories of electrons whose ranges were comparable to or greater than their cyclotron radii. In MRT at the European Synchrotron Radiation Facility (ESRF), the polyenergetic X-ray (white) beam has a mean energy of 07 kev and a maximum intensity at 83 kev (refer to figure 5.4). According to the simulation results of first generation electrons in figure 6.2, most secondary electrons have an energy less than 30 kev and a range (in perspex) of less than 5 µm. As an electron loses energy the radius of curvature of its path decreases. This begs the question of whether the application of a magnetic field during MRT could First generation electron spectrum of the ESRF white beam simulated with Monte Carlo PENELOPE using 0 8 primary photon histories. 39

164 40 Figure 6.: Impact of different types of interaction on the lateral dose profile of a single microbeam (25 µm wide) obtained with the ESRF white beam. Curve plots the microbeam profile comprising all interaction contributions. Curves 2, 3, and 4 plot the profile with supression of the photoelectric effect, Compton scattering, and electron tracking, respectively [25]. alter the low-energy electron distribution to produce a change in the dose profile of microbeams, and in particular, the peak-to-valley dose ratio (PVDR). According to figure 3., the range of a 00 kev electron becomes smaller than its cyclotron radius (in water) at magnetic fields less than about 7 T. For electrons below 00 kev, the range decreases at a faster rate than the reduction in cyclotron radius at a given magnetic field. Therefore, we would only expect to see an effect on the electron distribution and PVDR at magnetic fields of about 0 T or stronger. However, an EGS4 Monte Carlo study by Orion et al. [02] has shown that a 6 T longitudinal magnetic field applied to a single 20 kev microbeam (30 µm wide) can reduce the penumbral width by a few microns. This result contradicts our hypothesis as the range of a 20 kev electron is about one order of magnitude smaller than its cyclotron radius at 6 T. Absent from the literature are other studies confirming this effect.

165 First generation electron spectrum of the ESRF white beam Number of electrons Energy (kev) Figure 6.2: Simulated first generation electron spectrum of the white beam (in perspex). This chapter uses a combination of experiments and Monte Carlo PENELOPE simulations to investigate the effect of transverse and longitudinal magnetic fields on the lateral dose profiles and PVDRs of microbeams. Measurements of peak and valley dose were performed separately with both MOSFET and radiochromic film dosimetry. MOS- FET dosimetry was discussed in chapter 5 (refer to section 5..2). Radiochromic film comprises monomer crystals in a gel fixed to a Mylar substrate [03]. When irradiated, the energy deposition of particles initiates polymerisation of the monomers causing the film to change colour from light to dark blue. The dosimetry in the present work used HD-80 Gafchromic film 2, which has a high spatial resolution of around 600 line pairs per mm [88]) and a dose range between 0 and 400 Gy. The dose response is linear below about 250 Gy [04], although it is possible to use the film at higher doses provided one uses appropriate dose calibration curves to interpret the results [03]. Since radiochromic film continues to polymerise for several hours post-irradiation, the film analysis 3 was performed the day after exposure. 2 HD-80 Gafchromic film manufactured by ISP Technologies, NJ, USA. 3 Film analysis used an Epson scanner and a set of calibration films to convert optical density to dose.

166 Materials and methods The magneto-mrt experiments were conducted on the ID-7 biomedical beamline at the ESRF using three different magnet devices. 4 Each device was capable of producing either a transverse or longitudinal magnetic field up to a few Tesla. Measurements of the peak and valley doses, and hence, the PVDR were obtained with either Gafchromic film or a MOSFET embedded in a perspex phantom (perspex has a similar density to that of a human brain) Magneto-MRT with a transverse magnetic field The transverse magnetic field device used in the magneto-mrt experiments is shown in figure 6.3. The device comprises a pair of square NdFeB permanent magnets 5, each cm 3 (width height depth) with a surface field of T at the centre. A magnet pole separation of 0.5 cm generated a T static transverse magnetic field 6, where the direction of the field was orientated towards the handle of the device. For magneto-mrt measurements, the magnet device was mounted on the goniometer stage (inside the MRT experiment hutch) as shown in figure 6.3. A MOSFET was positioned at 0.9 cm depth in a cm 3 (width height depth) perspex phantom, which was wedged between the magnet poles (0.5 cm separation). The lateral dose profile of an array of three microbeams (each 25 µm wide, µm high, and separated by 42 µm) was measured with the T transverse magnetic field using a wiggler gap of 75 mm (instead of the minimum gap of 24.8 mm often used for MRT). The larger gap reduced the intensity of the beam so that the entire dose profile could be measured with a single MOSFET. At the completion of the scan, the wiggler gap was reduced to 24.8 mm and peak and valley dose measurements of the microbeam array were obtained in the presence and absence of the T transverse magnetic field. 4 Magnet devices constructed at the Centre for Medical Radiation Physics, University of Wollongong, Australia. 5 Square NdFeB magnets supplied by JWB Engineering, Bulli, NSW Australia. 6 Magnetic field measured using a Daley electronics Pty Ltd Teslameter T-22A.

167 43 Figure 6.3: Photos of the T transverse magnetic field device used for magneto-mrt experiments (direction of magnetic field is towards the handle). The magnet device (right) was mounted on the goniometer stage, where a perspex phantom containing a MOSFET was wedged between the magnet poles (left). For the peak dose measurements, the MOSFET was moved into the centre of the middle peak in the array (peak 2), where it was subjected to a 0.03 s pulse of radiation. Valley dose measurements were performed in the centre of the valley regions to the left and right of peak 2, V 2 and V 23 respectively, using radiation pulses of 3 s duration. For peak and valley dose measurements obtained in the absence of magnetic field, the magnet apparatus was replaced by a pair of steel dummy magnets of the same dimensions and separation to maintain scatter conditions. All peak and valley dose measurements were normalised to the synchrotron storage ring current and radiation exposure time. PVDRs were calculated from the peak and valley dose measurements obtained with and without magnetic field.

168 Magneto-MRT with a longitudinal magnetic field Permanent magnet devices The influence of a longitudinal magnetic field on the dose profiles of microbeams was investigated with a modified version of the above transverse magnetic field device. As illustrated in figure 6.4, a 0.3 cm diameter hole was drilled through the centre of each NdFeB magnet to allow passage of the microbeam array parallel to the magnetic field. A pair of focus cones were fixed to the inside surface of each magnet to concentrate the magnetic field lines, where a separation of 0.5 cm produced a field strength of about T. S N microbeams Figure 6.4: Illustration of the T longitudinal magnetic field device used for magneto- MRT experiments. A 0.3 cm diameter hole was drilled through the centre of the permanent magnets to allow the passage of microbeams parallel to the direction of magnetic field. Film dosimetry was used to obtain the lateral dose profile of an array of three microbeams (each 25 µm wide, µm high, and separated by 42 µm) in the presence and absence of a longitudinal magnetic field at different depths in perspex. For the profiles obtained with magnetic field, strips of Gafchromic film 7 were placed between 0. cm-thick perspex sheets. These sheets were wedged between the magnet focus cones 7 Strips of Gafchromic film (0 µm thick) were cut from one sheet and orientated in the same direction to minimise variation in dose response.

169 45 where dose profiles of the array were obtained at 0., 0.2, 0.3, and 0.4 cm depths. The effect of magnetic field on the peak profile of microbeams was investigated with an MRT peak dose of 500 Gy. The effect on the valley dose, on the other hand, was investigated with an MRT peak dose of Gy in order to raise the level of valley dose to sit within the sensitive range of the Gafchromic film. For measurements in the absence of magnetic field, the magnet device was replaced with a pair of dummy magnets to maintain similar scattering conditions. These were fashioned from steel (similar density to NdFeB) with the same dimensions as the permanent magnets. A stack of 0. and 0.2 cm-thick perspex sheets were wedged between the dummy magnets, where strips of Gafchromic film were placed at depths of 0., 0.2, 0.7,., and.2 cm (separation between dummy magnets was adjusted to allow dose profiles to be measured at depths beyond 0.5 cm). Prior to constructing the above longitudinal magnet device, a series of Monte Carlo simulations were performed to investigate whether the passage of microbeams through the magnet device would generate any additional scattering. The simulations used a model of the T longitudinal magnet device described above, using three different magnet materials: NdFeB, perspex, and air. This was done to compare the scattering contributions of the NdFeB magnets to no magnets (i.e. air replacing the magnets), and also the effect of more back scattering material (i.e. perspex replacing the magnets). A cylindrical scoring volume of 0.3 cm diameter 5.6 cm depth occupied the cavities inside the magnets and part of the region between the magnets. The section inside magnet and magnet 2 (magnet was upstream of magnet 2) was modelled as air, and the section between the magnets was modelled as perspex. The remaining volume between the magnets, not already occupied by the cylindrical perspex volume, was modelled as air. The array of three microbeams was approximated as a pencil beam of 850 µm (i.e. diameter equal to width of microbeam array). The initial direction of the beam was along the central axis, and the photon energy was sampled from the ESRF white beam spectrum. The

170 46 simulations were performed with electron and photon energy cutoffs of 0. and kev respectively, and 0 8 primary photon histories. The dose was scored on axis in cylindrical bins of 0.5 cm diameter and 0.05 cm depth. Figure 6.5 (a) plots the depth-dose profile of the pencil beam for different magnet materials (NdFeB, perspex, and air) in three regions along central axis: air cavity (inside magnet ), perspex phantom (between the magnets), and air cavity 2 (inside magnet 2). The simulations were repeated with the air cavity inside magnet 2 replaced with perspex to investigate the effect of additional backscattering material. The corresponding dose profile obtained for this setup is shown in figure 6.5 (b). The depth-dose profile obtained with NdFeB magnets exhibited up to 20% larger dose in both air cavities than the profiles obtained with perspex or air magnets. When perspex was inserted into air cavity 2, the depth-dose profiles in this region were the same as those obtained in the absence of magnets (i.e. air). Replacing the NdFeB magnet material with perspex resulted in the same depth-dose profile (within uncertainties) as that obtained without magnets. Simulations were also performed to determine the effect of magnet scatter contributions on the radial dose inside the air cavities and perspex phantom. For these simulations, the dose was scored in concentric cylindrical volumes whose annuli were separated by cm using identical simulation parameters as used previously. Figure 6.6 (a) plots a ratio of the radial dose obtained with and without NdFeB magnets at: the exit of air cavity (i.e cm depth), and 4 mm depth in perspex (i.e and 2.90 cm depth), and at the entrance to air cavity 2 (i.e cm depth). The simulations were repeated replacing the air in cavity 2 with perspex, to provide additional scattering material. A plot of the radial dose at the same depths is shown in figure 6.6 (b). Simulations were also performed to obtain the radial dose with and without perspex magnets (instead of NdFeB). A ratio of the radial dose in the presence and absence of NdFeB magnets is shown in figure 6.6 (c).

171 47 Scatter contributions from different magnet materials Dose (D/D max ) (a) NdFeB perspex air air cavity perspex phantom air cavity Depth (cm) Scatter contributions from different magnet materials Dose (D/D max ) (b) NdFeB perspex air air cavity perspex phantom Depth (cm) perspex phantom Figure 6.5: Scatter contributions from different magnet materials. Figure (a) plots the depth-dose profile of a pencil beam simulated with different magnet materials (NdFeB, perspex, and air) in three regions along central axis: air cavity, perspex phantom, and air cavity 2. Figure (b) plots the depth-dose profile with perspex replacing the air in cavity 2.

172 48 Dose (NdFeB / air) (a) air cavity mm perspex 4mm perspex air cavity 2 NdFeB magnets: effect of scattering on radial dose Radius (cm) Dose (NdFeB / air) (b) air cavity mm perspex 4mm perspex perspex phantom Radius (cm) Dose (perspex / air) (c) air cavity mm perspex 4mm perspex air cavity 2 Perspex magnets: effect of scattering on radial dose Radius (cm) Figure 6.6: Effect of magnet scatter contributions on the radial dose. Figure (a) plots a ratio of the radial dose with and without NdFeB magnets, at the following depths: 2.48 cm (exit of air cavity ), 2.60 and 2.90 cm ( and 4 mm depth in perspex), and 3.02 cm (entrance to air cavity 2). Figures (b) and (c) plots the corresponding radial dose with perspex magnets instead of NdFeB, and perspex replacing the air in cavity 2.

173 49 Inside the perspex phantom at and 4 mm depth, the ratio of radial dose with and without NdFeB magnets is unity. A ratio of unity is also observed inside the air cavities up to a radial distance of about 0.05 cm from the central axis. Beyond this distance, the ratio increases with increasing radial distance, whereas at the interface between the air cavity and magnet (0.5 cm) the radial dose with magnets is a factor of two larger than that obtained without. Replacing the air in cavity 2 with perspex reduced the ratio to unity. Replacing the NdFeB magnets with perspex (with air in cavity 2) resulted in ratios of unity at all depths. Additional dose contributions near the interface between the air cavities and NdFeB magnets is due to scattered photons and electrons from interactions in the magnets. The larger radial dose in air cavity 2 than in air cavity was due to the range of scattering angles at which the particles emerged from the perspex phantom between the magnets. When the air in cavity 2 was replaced with perspex, most of these scattered particles were attenuated prior to reaching the magnet material (range of a 00 kev electron in perspex is 0.05 cm), thereby reducing the ratio to unity. Inside the perspex phantom, the scatter contributions from of magnet material were shown to have no effect on either the depth-dose or radial dose. One can therefore be confident that the passage of microbeams through the longitudinal magnet device has no effect on the dosimetry performed in the perspex phantom between the magnets. The availability of stronger permanent magnets led to the construction of a second longitudinal magnetic field device for magneto-mrt experiments. The interest in stronger magnetic fields is due to electrons having smaller cyclotron radii, and hence, the potential for greater effect. As shown in figure 6.7, the device comprises a pair of cylindrical NdFeB magnets 8, each 0 cm diameter 5 cm depth with a surface field of 2 T. A.0 cm diameter hole through the centre of each magnet allowed the passage of microbeams parallel to the magnetic field. The magnets were fixed to a U-shaped iron circuit to maximise magnetic flux. A steel focus cone was fixed to the surface of each 8 Neo Ring N42-type cylindrical NdFeB magnets supplied by AMF Magnetics, Mascot, NSW Australia.

174 50 magnet to concentrate the field lines along the axis. These focus cones were separated by cm of air to produce a maximum flux6 of about 2 T. MATLAB simulations9 estimated a maximum field of 2.2 T between the focus cones, as shown in figure 6.8. Figure 6.7: Photo of the 2 T longitudinal magnetic field device used for magneto-mrt experiments. The device comprises a pair of cylindrical NdFeB permanent magnets with steel focus cones and a U-shaped iron circuit to maximise magnetic flux. The lateral dose profile of an array of 24 microbeams (each 25 µm wide, µm high, and separated by 42 µm) was obtained with and without a 2 T longitudinal magnetic field. For the measurements with magnetic field, four strips of Gafchromic film were positioned at 0.2, 0.4, 0.6, and 0.8 cm between a stack of 0.2 cm-thick perspex sheets wedged in the cm gap between the focus cones. For measurements conducted in the absence of field, the magnet device was replaced with a set of steel dummy magnets of identical dimensions to maintain the similar scattering conditions. 9 MATLAB simulations performed by Brad Oborn, a fellow PhD student at the Centre for Medical Radiation Physics, University of Wollongong, Australia.

175 5 Figure 6.8: MATLAB simulation of the magnetic flux produced by the longitudinal magnetic field device. A maximum field of 2.2 T was calculated between the focus cones, which were separated by cm Magnet coil device The influence of a longitudinal magnetic field on the PVDR of microbeams was also investigated with MOSFET dosimetry. The insufficient space between the focus cones in the above permanent magnet devices led to the construction of a magnet coil which could accommodate the MOSFET aligned in the direction of magnetic field. The advantage of using a magnet coil over permanent magnets is the unobscured and variable strength of longitudinal magnetic field, which is proportional to current, and the ability to perform dose measurements over a wider range of depths (i.e. not limited by the distance between magnets). Furthermore, because the magnetic field is pulsed, the coil can also be used for dose measurements in the absence of a magnetic field. This eliminates any anomalies in scattered dose contributions that may arise with the use of dummy magnets.

176 52 The magnet coil 0 comprises 828 turns of cm diameter copper wire, with a 2.5 cm diameter air core at the coil centre. It measures 6.5 cm diameter 7.0 cm depth and has a resistance and inductance of Ω and 29 mh respectively. When a current of 200 A was pulsed through the coil,.3 and 2.5 T magnetic fields were estimated at the centre of the coil s surface and middle of the air core, respectively. These estimates were obtained by measuring the magnetic flux density at the surface of the coil with a low DC current. Knowing the magnetic flux, φ m, number of turns, N, and area of the coils, A, the magnetic field, B, was calculated from the expression B = φ m / NA. For a.0 A current, the magnetic field was T. Since magnetic field is proportional to current, 200 A of current through the coil will produce a magnetic field of about.3 T at the coil surface. Magneto-MRT measurements were performed with the coil mounted on an aluminium stage, which was fixed to the goniometer as shown in figure 6.9. Electrical wires connected the coil to a current pulser box on the floor of the experimental hutch, which contained a bank of µf capacitors (refer to appendix A for circuit diagrams and descriptions of the current pulser and time delay circuits). To ensure synchronisation of the pulsed magnetic field with the 30 ms beam delivery, a logic pulse was used to trigger the discharge of capacitors (i.e. pulsed magnetic field) at the instant the fast shutter opened (a diode pulse is used to activate the shutter opening). The relationship between the diode pulse and current pulse was monitored on an oscilloscope, as shown in figure 6.0, where the optimal time delay between pulses was an 80 ms lead of the current over the diode. The coincidence of the pulsed current and the induced magnetic field (measured with a Hall probe Teslameter) was monitored on an oscilloscope. The output is shown in figure 6.. The influence of the pulsed magnetic field on the dose profile of an array of 24 microbeams (each 50 µm wide, µm high, and separated by 42 µm) was investigated with MOSFET dosimetry. Peak and valley dose measurements were obtained with an 0 Magnet coil and current pulser circuit was constructed under the direction of Terry Braddock, an electrical engineer in the Centre for Medical Radiation Physics, University of Wollongong, Australia.

177 53 Figure 6.9: Photos of the magnet coil used for magneto-mrt experiments. The 828turn copper coil was mounted on the goniometer (left), where the cylindrical perspex phantom (housing the MOSFET) was inserted into the air core and secured to a perspex block behind the coil (right). current diode Figure 6.0: Oscilloscope output verifying the synchronisation of the current pulse (i.e. pulsed magnetic field) and the rectangular diode pulse (i.e. beam delivery).

178 54 magnetic field current Figure 6.: Oscilloscope output verifying the coincidence of the pulsed current (i.e. discharge of capacitors) and magnetic field. Delay between the current and diode pulses was adjusted to provide a maximum magnetic field during irradiation of the target. edge-on MOSFET positioned at. cm depth in a perspex cylindrical phantom of 2.5 cm diameter and 5 cm depth. The phantom was inserted into the core and secured to a perspex block, which was flush against the exit surface of the coil as shown in figure 6.9. The MOSFET (and coil) was moved to the centre of peak 2 (central microbeam) where it was subjected to pulses of radiation with and without the 2.5 T pulsed magnetic field. The change in threshold voltage (i.e. absorbed dose) measured by the MOSFET reader was normalised to the synchrotron storage-ring current and exposure time. Measurements were also performed with the MOSFET at the microbeam edge (i.e. ±25 µm from peak centre) and in the valley region at ±50, ±00, and ±206 µm from peak centre. The duration of radiation pulses were 0 ms at the centre and edges of the peak, 30 ms at ±50 µm, and 00 s in the middle of the valley (±206 µm) Magneto-MRT Monte Carlo simulations Monte Carlo PENELOPE simulations were performed to supplement the MOSFET and Gafchromic film results. The dose profile of a single microbeam and an array of three

179 55 microbeams were simulated with and without a 2 T magnetic field (i.e. same approximate field strength as used in the above magneto-mrt experiments). Additional simulations were performed with stronger magnetic fields of 0, 20, 50, and 00 T to investigate the dependence of PVDR on field strength. The simulations were performed with the ESRF white beam spectrum (refer to figure 5.4), and included a model of the Tecomet R multislit collimator, distributed synchrotron source, 33 m source to multislit collimator distance, and m air region between the collimator and phantom (details of the modelled beamline components appear in chapter 7). Profiles obtained in the presence of transverse and longitudinal magnetic fields were scored at 0.9 and. cm depth (in perspex), respectively, to facilitate comparison with measured profiles. Dose was scored in bin volumes of cm 3 (width height depth). The simulations were performed with electron and photon transport cutoffs of kev and a total of 0 0 primary photon histories. The average PVDR of the central peak in an array of three microbeams (peak 2) was calculated using the dose in the central bin of the peak region and an average of dose in four bins about the valley midpoint (i.e. ±206 µm from peak centre). 6.3 Results and Discussion 6.3. Effect of a transverse magnetic field on microbeam profiles Figure 6.2 shows the dose profile of an array of three microbeams subjected to a T transverse magnetic field measured with a MOSFET at 0.9 cm depth (in perspex). The variations in the peak intensity and FWHM of microbeams are related to the construction of the multislit collimator and its alignment. The collimator comprises a number of layers of thin tungsten foils glued together, where the rough inside edges of the apertures are known to produce up to 4 µm differences in the full-width at half-maximum (FWHM) of microbeams [23]. While these variations have little influence on the intensity of microbeams, the alignment of the multislit collimator (with respect to the beam) does, as demonstrated with Monte Carlo simulation in the following chapter.

180 56.2 Measured dose profile with a T transverse magnetic field MOSFET response (mv/ma) Position (µm) Figure 6.2: Lateral dose profile of an array of three microbeams measured with a MOS- FET at 0.9 cm depth (in perspex) in the presence of a T transverse magnetic field. Figures 6.3 (a) and (b) plot the dose profiles of valleys V 2 and V 23 (to the left and right of the central microbeam, respectively) with and without a T transverse magnetic field. These profiles were measured with a MOSFET at 0.9 cm depth in perspex using a wiggler gap of 24.8 mm (standard MRT conditions). The V 2 and V 23 valley dose profiles measured in the absence of field exhibit differences in dose at the centre and left edges of their profiles. The valley profiles obtained in the presence of a T transverse magnetic field, on the other hand, are almost identical. These profiles exhibit a reduction in dose and widening of the valley, when compared with the valley profiles obtained in the absence of field, suggesting a narrowing of the peak. Considering the valley profiles obtained with and without magnetic field were acquired on different days, one cannot make a direct comparison between the two without examining the effect on peak dose. The impracticality of measuring the peak profile (i.e. peak dose intensity severely reduces a MOSFET s lifetime) led to dose measurements at the peak centre in the presence and absence of magnetic field. Figures 6.4 (a) and (b) plot V 2 and V 23 valley dose at 0.9,.9, and 2.8 cm depth (in perspex) with and without a T transverse magnetic field. Figures 6.4 (c) and (d) plot the peak dose and PVDR of the central microbeam (peak 2) with and without magnetic field at the same depths.

181 57 Effect of a transverse field on valley V 2 MOSFET response (mv/ma) (a) zero T Position (µm) Effect of a transverse field on valley V 23 MOSFET response (mv/ma) (b) zero T Position (µm) Figure 6.3: Effect of a T transverse magnetic field on the valley dose of an array of three microbeams. Figures (a) and (b) plot the dose profiles of valley regions V 2 and V 23 (i.e. left and right of the central microbeam, peak 2) respectively, measured with a MOSFET at 0.9 cm depth (in perspex) in the presence and absence of magnetic field.

182 58 MOSFET response (mv/ma/s) (a) Measured V 2 valley dose with depth Depth (cm) zero T MOSFET response (mv/ma/s) (b) Measured V 23 valley dose with depth Depth (cm) zero T Figure 6.4: Valley dose for an an array of three microbeams measured with a MOSFET at 0.9,.9, and 2.8 cm depth (in perspex). Figures (a) and (b) plot the dose at the centre of valleys V 2 and V 23 (i.e. left and right of the central microbeam, peak 2) respectively, in the presence and absence of a T transverse magnetic field.

183 59 MOSFET response (mv/ma/s) (c) Measured peak dose with depth Depth (cm) zero T (d) Measured PVDR with depth zero T PVDR Depth (cm) Figure 6.4: Peak dose and PVDR for the central microbeam in an array of three microbeams (peak 2) measured with a MOSFET at 0.9,.9, and 2.8 cm depth (in perspex), in the presence and absence of a T transverse magnetic field, is shown in figures (c) and (d) respectively. The PVDR was calculated using the dose at the centre of peak 2 and valleys V 2 and V 23 on either side.

184 60 The peak and V 2 and V 23 valley regions exhibit a reduction in dose with depth. Unfortunately, only three depths were investigated owing to beamtime constraints. Ideally, more measurements at different depths would have been performed to improve the overall quality of the data. Nevertheless, these data exhibit trends consistent with those seen in both the previous chapter and literature [25]. The reduction in peak dose with increasing depth is due to photon attenuation. Valley dose can also be seen to decrease with depth owing to the presence of fewer scattered photons, and hence, secondary electrons. The faster rate of dose reduction in the peak than in the valley gives rise to the reduction in PVDR with depth. This is consistent with the Monte Carlo results in the previous chapter and literature [25, 32, 85]. It is difficult to make a direct comparison between the results obtained with and without magnetic field as they were performed on different days. The reason for this is that daily adjustments are made to the alignment of the MOSFET and multislit collimator (i.e. microbeam array) to correct for any shift in the synchrotron beam. The valley profiles in figure 6.3 are testimony to this, where the V 2 and V 23 profiles obtained with magnetic field are almost identical, while those produced without magnetic field differ at the centre and left edges of their profiles. In retrospect, these measurements should have been performed consecutively on the same day to minimise any variations in alignment. Monte Carlo simulations were performed to determine the effect of a transverse magnetic field on the PVDR of a microbeam array. Figure 6.5 plots the simulated dose profile of an array of three microbeams scored between 0.8 and.0 cm depth in perspex (to match the 0.9 cm depth of the MOSFET) in the presence and absence of a 2 and 00 T transverse magnetic field. PVDRs of 600 ± 50, 590 ± 50, and 580 ± 50 were calculated for the profiles obtained with zero, 2, and 00 T respectively, using the dose at the centre of peak 2 and an average of four bins in the middle of the two adjacent valleys (uncertainties in the peak and valley dose were 3% and 8% respectively). The PVDR and peak and valley doses were within their uncertainties, which suggests the dose profiles of microbeams are unaffected by the presence of a transverse magnetic field.

185 6 Simulated effect of a transverse magnetic field on microbeams zero 2T 00T Dose (D/D max ) Distance (cm) Figure 6.5: Simulated effect of a transverse magnetic field on the dose profile of an array of three microbeams. A plot of the microbeam array scored between 0.8 and.0 cm depth (in perspex) in the presence and absence of a 2 and 00 T transverse magnetic field Effect of a longitudinal magnetic field on microbeam profiles Figure 6.6 plots the lateral dose profile of an array of three microbeams (each 25 µm wide, µm high, and separated by 42 µm) measured in the absence of magnetic field with Gafchromic film at 0., 0.2, 0.7,., and.2 cm depths (in perspex). These profiles exhibit a reduction in peak dose with increasing depth due to the attenuation of photons. Dose profiles of the microbeam array in the presence of a T longitudinal magnetic field were also measured with Gafchromic film. Owing to the 0.5 cm separation between the magnet focus cones, these profiles were limited to depths of 0., 0.2, 0.3, and 0.4 cm. Figure 6.7 plots the peak dose of the central microbeam with depth in the presence and absence of magnetic field. Despite larger peak doses with magnetic field, the values were within the uncertainties of those obtained in the absence of field. Further measurements comparing the peak and valley doses of an array of three

186 62 Dose (Gy) Measured microbeam profiles with depth (in perspex) 0.cm 0.2cm 0.7cm.cm.2cm Distance (µm) Figure 6.6: Dose profile of an array of three microbeams measured with Gafchromic film at 0., 0.2, 0.7,., and.2 cm depths (in perspex) in the absence of magnetic field. microbeams in the presence and absence of a T longitudinal magnetic field is shown in figures 6.8 (a) and (b) respectively. The profiles were measured with Gafchromic film at 0.2 cm depth (in perspex) using an MRT peak dose of 500 Gy for the peak profiles, and Gy for the valley profiles (in order to raise the level of valley dose to sit within the sensitive range of the film). The presence of a T longitudinal magnetic field yielded larger peak doses (up to 30%) and smaller valley doses (up to 25%), which suggests a reduction in the lateral spread of electrons into the valleys (i.e. reduction in the orthogonal component of electron trajectories with respect to the direction of magnetic field). This gives rise to larger PVDRs, as shown in table 6., which compares the PVDRs of the central microbeam (peak 2) at 0. and 0.2 cm depth (in perspex) in the presence and absence of magnetic field. A comparison of the peak dose and valley dose (averaged over 0 µm at the centres of valleys V 2 and V 23 ) is also shown. The PVDR uncertainty was calculated as the square of the relative uncertainties in the peak and valley dose, both of which were 0%.

187 Measured peak dose with depth (in perspex) zero T Dose (Gy) Depth (cm) Figure 6.7: Peak dose of the central microbeam in an array of three microbeams (peak 2) with depth. A plot of the peak dose measured with Gafchromic film at depths (in perspex) of 0., 0.2, 0.3, and 0.4 cm in the presence of a T longitudinal magnetic field, and 0., 0.2, 0.7,., and.2 cm in the absence of magnetic field. Table 6.: Peak and valley doses and PVDR of the central peak (peak 2) in an array of three microbeams. Peak and valley doses were measured with Gafchromic film at 0. and 0.2 cm depth (in perspex) in the presence and absence of a T longitudinal magnetic field, B. 0. cm depth 0.2 cm depth B = zero B = T B = zero B = T Dose Peak (Gy) 470 ± ± ± ± 50 Dose Valley (Gy) 0.74 ± ± ± ± 0.06 PVDR 630 ± ± ± ± 20

188 (a) Effect of a magnetic field on the peak dose zero T Dose (Gy) Distance (µm) (b) Effect of a magnetic field on the valley dose zero T Dose (Gy) Distance (µm) Figure 6.8: Effect of a T longitudinal magnetic field on the peak and valley doses of an array of three microbeams. Figures (a) and (b) show the peak and valley dose profiles, respectively, measured with Gafchromic film at 0.2 cm depth (in perspex) in the presence and absence of magnetic field.

189 65 The availability of stronger magnets led to the construction of a 2 T permanent magnet device (refer to section ) to investigate the potential for further gains in PVDR. For these experiments, the dose profile of an array of 24 microbeams was measured with Gafchromic film at 0.2, 0.4, 0.6, and 0.8 cm depth in perspex. Profiles were also measured at these depths in the absence of magnetic field using a pair of steel dummy magnets. A comparison of the profiles obtained with and without magnetic field revealed no consistent differences in the peak or valley dose, and hence, no change in the PVDR. This contradicted earlier film results with a T longitudinal magnetic field, which showed an increase in the PVDR in the presence of magnetic field. The discrepancy between Gafchromic film results may stem from the non-uniform energy response across individual sheets of film which can be as much as ±8% [04]. The discrepancy in film results motivated the use of an alternative dosimeter to perform a final investigation of the effect of a longitudinal magnetic field on the dose profiles of microbeams. The edge-on MOSFET dosimeter was chosen for these measurements as it has a high spatial resolution of about µm. Magneto-MRT experiments were performed with a magnet coil (built to accommodate the MOSFET and perspex phantom within its air core) which produced a maximum longitudinal magnetic field of 2.5 T. Peak and valley dose measurements were obtained for an array of 24 microbeams (each 50 µm wide, µm high, and separated by 42 µm) with and without a magnetic field. These measurements were performed with the MOSFET in the centre of peak 2 and at the right edge of the peak (i.e. 25 µm from peak centre). Penumbral and valley dose measurements were also obtained at 50 and 206 µm from the peak centre, respectively. Exposure times of 0.0, 0.03, and 0 s were used for dose measurements in the peak, penumbral, and valley regions respectively. For each position in the peak 2 profile, dose measurements in the presence and absence of magnetic field were the same within uncertainties. Different time delays between the current and diode pulses (i.e. pulsed magnetic field and beam delivery) similarly, had

190 66 no affect. These results were consistent with those obtained with the 2 T permanent magnetic device and Gafchromic film. They also verify the hypothesis that the range of the electrons must be comparable to or greater than their cyclotron radii in order to see an effect. At magnetic fields of or 2 T, the range of a 00 kev electron is an order of magnitude smaller than its cyclotron radius. For a 0 kev electron, this difference is two orders of magnitude, where a magnetic field of about 00 T is needed to reduce its cyclotron radius to a distance comparable with its range. The presence of a longitudinal magnetic field of a few Tesla has no effect on the dose profiles nor the PVDRs of microbeams. The strength of magnetic field needed to produce an effect can be seen in the following Monte Carlo results. Simulated effect of a longitudinal magnetic field Dose (D/D max ) zero 2T 0T 20T 50T 00T Distance (cm) Figure 6.9: Simulated effect of a longitudinal magnetic field on the dose profile of a single microbeam. A plot of the profile scored between.0 and.2 cm depth (in perspex) in the presence and absence of a 2, 0, 20, 50, and 00 T magnetic field. Figure 6.9 compares the dose profile of a single microbeam (25 µm wide and µm high) scored between.0 and.2 cm depth (in perspex) with and without a 2, 0, 20, 50, and 00 T longitudinal magnetic field. The dose profiles obtained in the

191 67 presence of 2 and 0 T magnetic fields are almost identical to those produced in the absence of field. Microbeams subjected to magnetic fields of 20 T or greater, on the other hand, exhibit reductions in their penumbral and valley doses. Larger reductions were observed with stronger magnetic fields due to a reduction in the lateral scattering of electrons as their ranges become comparable to or greater than their cyclotron radii (refer to figure 3.). The reductions in valley dose correspond with increases in PVDR of as much as 5%. Noting that the valley dose of an array comprises a superposition of overlapping dose tails from individual microbeams, additional simulations were performed with an array of three microbeams (each 25 µm wide, µm high, and separated by 42 µm) to determine whether a reduction in valley dose still existed. Figure 6.20 (a) compares the dose profile of the array scored between.0 and.2 cm depth (in perspex) in the presence and absence of a 2, 0, 20, 50, and 00 T longitudinal magnetic field. The profiles have been normalised to the peak dose in the central microbeam of the array (i.e. D max ). A ratio of the dose profiles obtained with and without magnetic field is shown in figure 6.20 (b). The microbeam dose profiles obtained in the presence of 20, 50, and 00 T longitudinal magnetic fields exhibit penumbral dose reductions of as much as 20, 65, and 85% respectively. The 2 and 0 T profiles also exhibit minor reductions in penumbral dose, however, these are within the 8% uncertainties. In the centre of the valleys (i.e. ±206 µm), the reduction in dose is substantially lower than that near the peak, where profiles obtained in the presence of 20, 50, and 00 T magnetic fields exhibit reductions of approximately 7, 0, and 5% respectively. As doses have been normalised to peak dose, valley dose reductions correspond to PVDR increases of 7, 0, and 5% respectively, as shown in figure 6.2. The higher PVDRs obtained with stronger magnetic fields is due to the smaller cyclotron radii of electrons, confining the lateral component of their trajectories and thereby reducing valley dose.

192 68 Effect of a longitudinal magnetic field on microbeams Dose (D/D max ) (a) zero 2T 0T 20T 50T 00T Distance (cm) Effect of a longitudinal magnetic field on microbeams (b) Dose (B/B=0) T 0T 20T 50T 00T Distance (cm) Figure 6.20: Simulated effect of a longitudinal magnetic field on the dose profile of an array of three microbeams. Figure (a) shows the dose profile of the array scored between.0 and.2 cm depth (in perspex) in the presence and absence of a 2, 0, 20, 50, and 00 T magnetic field. A ratio of the dose profile with and without magnetic field is plotted in figure (b).

193 Effect of a longitudinal magnetic field on the PVDR 700 PVDR Magnetic field (T) Figure 6.2: Simulated effect of a longitudinal magnetic field on the PVDR of an array of three microbeams. A plot of the PVDR of the central microbeam against magnetic field strength, using the dose profiles scored between.0 and.2 cm depth (in perspex). 6.4 Conclusion The presence of a transverse or longitudinal magnetic field of a few Tesla was shown both experimentally and theoretically to have no effect on the dose profiles of microbeams. According to Monte Carlo PENELOPE simulations, longitudinal magnetic fields greater than 0 T are needed to produce an effect. This contradicts Orion s ESG4 result which shows a reduction in the penumbral dose (of a few microns) for a single 20 kev microbeam subjected to a 6 T longitudinal magnetic field. Apart from the different photon beam energies, the difference between the two simulation results may stem from the modelling of polarisation effects. While modelling of photon polarisation for Compton scattering is included in the EGS4 distribution, it is not accounted for in the 2003 version of the PENELOPE code used for this work. However, considering the penumbral dose for a 20 kev microbeam is predominantly produced by photoelectric interactions (refer to figure 5.4), any polarisation effect at these energies are negligible. A

194 70 direct comparison of the codes, which is now possible with the recent inclusion of photon polarisation in the 2008 version of PENELOPE, is needed to verify this hypothesis. The effect of 20, 50, and 00 T longitudinal magnetic fields on an array of three microbeams was to increase the PVDRs by 7, 0, and 5% respectively. The higher PVDRs are brought about by a reduction in the lateral spread of secondary electrons, whose ranges are comparable to or greater than their cyclotron radii. The application of a transverse magnetic field of up to 00 T, on the other hand, had no effect on the dose profile or PVDR of microbeams. This is because the direction of magnetic field is parallel with the lateral component of an electron s trajectory, and hence, only the orthogonal components of the electron s path are affected. It is therefore possible that sufficiently strong transverse magnetic fields may alter the depth-dose profile of microbeams. While the presence of magnetic fields of a few Tesla during MRT has no effect on electron distribution, it is possible that they may influence the repair mechanisms of tissue. Studies have shown the application of magnetic fields can influence the orientation of molecular domains in cell membranes, thus changing their structure and curvature [05] and potentially altering the diffusion of molecules across the membrane surface (a process critical to normal membrane function and antibody binding) [06]. In liquid water, the presence of static magnetic fields (between and 0 T) have also been shown to enhance the hydrogen bonds of water molecules, thereby improving their stability [07]. A study of breast cancer patients exposed to magnetic fields prior to irradiation reported substantial, and in some cases complete, tumour regression [08]. Could the application of a magnetic field before, during, or after MRT irradiation alter the repair mechanisms of brain tissue in such a way to improve the efficacy of the treatment?

195 CHAPTER 7 A MONTE CARLO STUDY OF THE INFLUENCE OF MRT BEAMLINE COMPONENTS ON MICROBEAM PROFILES 7. Introduction Monte Carlo simulation is a popular theoretical tool used to estimate the dose distribution in radiotherapy. It is particularly useful in Microbeam Radiation Therapy (MRT) as it allows the study of dose deposition on a micron scale which may otherwise be difficult to measure. However, its potential use in future MRT dose planning is currently hindered by an ongoing discrepancy between measured and theoretical dose profiles of microbeams. The need to resolve this discrepancy is driven by the desire to make MRT available to humans in the next few years. This chapter examines common simplifications in MRT modelling which may account for the differences between theoretical and measured dose. One simplification is the commencement of microbeam transport on the surface of the target, which neglects the effect of the synchrotron source, multislit collimator, and beam divergence between them. This work investigates the influence of these components on microbeam profiles, together with the effect of collimator alignment, interaction medium, and height of the scoring region. Many of the results appearing in this chapter have been published in a peer-reviewed journal article [09]. In MRT, a multislit collimator is placed in the path of the beam between the source and target, to shape the wide beam into a linear array of parallel, rectangular, micronsized X-ray beams (microbeams) for treatment. For more than a decade, numerous collimator designs have been trialled to investigate optimal microbeam characteristics for treatment. Before the advent of a multislit collimator, MRT irradiations were performed 7

196 72 with a single-aperture collimator and multiple exposures [29, 30, 32, 82, 83]. This timeintensive process increased the risk of target (small animal) movement, blurring the otherwise steep dose gradients at the edge of the irradiated microslices. The invention of the multislit collimator made it possible to deliver a large array of microplanar beams in a single fast exposure, thereby reducing the treatment time and broadening of irradiated microslices due to target movement. The first multislit collimator used for MRT at the European Synchrotron Radiation Facility (ESRF) was the Archer-type multislit collimator (AMSC) [0]. It comprised two stacks of alternating aluminium and gold foils, where microbeam width was determined by the lateral translation of one stack relative to the other [20, 23]. The AMSC s 0 µm variation in the full-width at half-maximum (FWHM) of microbeams led to its replacement by the Tecomet R variable-width collimator. As shown in figure 7., this collimator comprises two identical stacks, each containing 25 parallel, 00 µm wide, 8 mm deep air apertures separated by 300 µm wide tungsten teeth to produce 400 µm centre-to-centre spacing between adjacent microbeams [23]. Lateral translation of these motor-controlled stacks enables the width of microbeams to be adjusted. Originally constructed from a number of layers of thin tungsten foils glued together, the rough inside edges of the collimator apertures produced variations of up to 4 µm in the FWHM of microbeams [23]. Improved technology for the manufacture of collimators has led to the recent replacement of the multilayered tungsten foil stacks with solid tungsten-carbide blocks comprising smooth, wire-cut apertures. In the future, once optimal microbeam parameters for MRT have been determined, it may be desirable to replace the variable-width multislit collimator with a single-stack design whose apertures are of fixed width. Monte Carlo simulation has been used in MRT to estimate the peak-to-valley dose ratio (PVDR) across an array of microbeams with various X-ray beam energies, centreto-centre microbeam spacings, and depths of interaction [6, 9, 22, 23, 25, 32, 85, 87]. These studies have used the superposition of the dose profile from a single microbeam to

197 73 Figure 7.: Photo of the Tecomet R multislit collimator (left) which comprises two identical tungsten air stacks mounted in an aluminum frame. Each stack (right) contains 25 parallel, 00 µm wide, 8 mm deep apertures with 400 µm centre-to-centre spacing [23]. estimate the PVDR of microbeams. Bräuer-Krisch et al. compared the PVDR of a microbeam array measured with a MOSFET to that simulated with a modified version of the Monte Carlo GEANT code used at the Paul Scherrer Institute (PSI) [85]. The measured PVDRs were found to be within 5% of the theoretical values, despite the absolute peak and valley dose measurements being 20% lower than those obtained theoretically [22]. The authors attribute the difference to a ±30% fluctuation in the measured FWHM of microbeams emerging from the AMSC, and the modelling of identical planar rectangular microbeams. A later study by Siegbahn et al. [86] compared the dose profile of a microbeam array measured with Gafchromic film to that simulated with Monte Carlo PENELOPE. Measured valley doses were approximately double those obtained theoretically, corresponding to PVDRs of about half of the simulated values. The authors attribute the discrepancy to crude simplifications in the modelling of the real irradiation geometry (i.e. absence of a multislit collimator model, beam divergence, and polarisation of the synchrotron beam). A Monte Carlo EGS4 study by De Felici et al. used a 3 3 cm array of microbeams (25 µm wide and separated by 200 µm) to demonstrate the effect of the beam polarisation. While polarisation caused a 6% difference in the dose deposition at